Find the equation of a circle when its centre and radius are given: (i) Centre at and radius (ii) Centre at and radiu

Convert the following equations of circle into standard form and hence find their centre and radius: (i) (ii) (iii) -

Find the equation of the circle passing through the following sets of three non-collinear points: (i) (ii) (iii) wher

Find the equation of the circle with its centre lying on the line and passing through the points and . --- Background

Find the equation of the circle passing through the points and and whose centre lies on the line . --- Background and

Find the equation of the circle passing through the point and touching the line at the point . --- Background and Expl

A circle touches the line at the point and passes through the point of intersection of the lines and . Find the equat

Equations of two diameters of a circle are and and its radius is 5. Find the equation of the circle. --- Background an

A circle touches both the -axis and -axis in the first quadrant. Given that the area of the circle is square units, fin

The two points and lie on a circle. The centre of the circle lies on the perpendicular bisector of the chord . The dis

Find the equation of the circle passing through the intersection of the circles: and passing through the point . Hint: T

The diagram shows a rectangle and the circles and . Both the circles touch each other and three sides of the rectangle

A circle has its centre at the point and a line touches the circle. The point lies on the line touching the circle. Th

The three lines , , and touch a circle. Find the centre of the circle and the equation of the circle. --- Background an

Find the points of intersection of the given line and the circle. (i) and (ii) and (iii) and --- Background and Ex

The equation of a circle is and the equation of a line is . Find the value(s) of such that the line: (i) Intersects th

Find the equations of the tangent lines to the circle that are perpendicular to the line . --- Background and Explanati

Find the equations of the tangent and normal to the circle at the point . --- Background and Explanation To find the eq

Find the equation of the tangent to the circle at the point on the circle with abscissa . --- Background and Explanatio

Find the equation of the normal to the circle at the point on the circle with ordinate . --- Background and Explanation

Find the equation of the common tangent to the circles: given that they touch each other externally. --- Background and

Show that the tangent line at any point of the circle is always perpendicular to the radial line through point . --- Ba

and are two points on the circle . 1. Find the point of intersection of the tangents to the circle at and . 2. Show th

A normal line cuts the circle with centre at at the point . Find the other point of intersection of the normal to the c

Check whether the given point lies inside, outside, or on the given circle: (i) ; (ii) ; (iii) ; --- Background an

Find the length of the tangent to the circle from the point lying outside the circle. --- Background and Explanation T

Find the length of the tangent to the circle drawn from the point lying outside the circle. --- Background and Explana

The point lies outside the circle . Find the equations of the tangents to the circle drawn from point and find the poi

A quadrilateral is circumscribing a circle. Prove that: --- Background and Explanation This proof is based on the geome

Two tangents are drawn from a point lying outside the circle . Find the area of the shaded region. --- Background and E

From a point lying outside the circle, a tangent and a secant line are drawn. Prove that: --- Background and Explanat

Find the focus, vertex, axis of symmetry, directrix, length of latus rectum, and end points of the latus rectum of the p

Find the equation of the parabola in each of the following cases: (i) Vertex at origin and focus (ii) Vertex and focus

Find the equation of the parabola with the focus at and the directrix given by the equation: --- Background and Explana

Find the coordinates of the vertex of each parabola by differentiating its equation on both sides and then solving for t

Find the points of intersection of the line and the parabola . Also, find the length of the chord intercepted by the pa

For what value(s) of does the line never touch or intersect the parabola ? --- Background and Explanation To determine

Find the value of () so that the line is tangent to the parabola: $$ y^{2}-2 y+3 x+7=0 $$ --- Background and Explanati

Prove that the line is tangent to the parabola . Also, find the point of contact. --- Background and Explanation To pro

Find the equation of the tangent and normal to the parabola at the point . --- Background and Explanation To find the e

Find the equation of the tangent and normal to the parabola at the point where the abscissa is 1. --- Background and Ex

Find the equation of the tangent and the normal to the parabola at the end points of its latus rectum. --- Background a

Let and be any two points on the parabola . Prove that the chord joining and is a focal chord if . --- Background an

Part (a): A tangent line is drawn to the parabola at any point . Prove that the line segment of the tangent cut off betw

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Prove that the tangent to the parabola at any point on the parabola makes equal angles with the line joining and its f

Prove that the semi latus rectum of a parabola is the harmonic mean between the segments of any focal chord. --- Backgro

Find the centre, vertices, co-vertices, foci, eccentricity, length and equation of major axis, length and equation of mi

From the given information, find the equation of the ellipse in each of the following cases: (i) Vertices and co-vertic

Find the coordinates of the vertices and co-vertices of the following ellipses by differentiating the equation on both s

Find the points of intersection of the line and the ellipse, and also find the length of the chord intercepted: --- Back

Find the value of () such that the line touches the ellipse . Also, find the point where it touches the ellipse. --- B

Find the equation of the tangent to the ellipse with slope 1. --- Background and Explanation To find the tangent to a c

Find the equation of the tangent to the ellipse which is perpendicular to the line . --- Background and Explanation To

Find the equations of the tangent and normal to the ellipse at the point . --- Background and Explanation To find the e

Find the equations of the tangents and normals to the ellipse at the point with ordinate . --- Background and Explanati

Prove that the tangent at any point to the ellipse makes equal angles with the lines joining that point with the foci (t

Find the centre, vertices, co-vertices, foci, eccentricity, length and equation of the transverse axis, length and equat

From the given information, find the equation of the hyperbola in each of the following cases: (i) Vertices: , ; conjuga

Find the vertices of the following hyperbolas by differentiating the given equation and solving for horizontal or vertic

Find the length of the chord intercepted by the line and the hyperbola . --- Background and Explanation To find the len

Find the value of so that the line is tangent to the hyperbola . --- Background and Explanation To find the condition

Find the equation of the tangent to the hyperbola which is parallel to the line . --- Background and Explanation To fin

Find the equation of the tangent to the hyperbola which is perpendicular to the line . Also, find the point of tangency

Find the equation of the tangent and normal to the hyperbola at the point . --- Background and Explanation To find the

Find the equations of the tangent and normal to the hyperbola at the point whose ordinate () is and the abscissa () is

Prove that the tangent at any point of the hyperbola makes equal angles with the lines joining the point with the foci o

The line is tangent to the hyperbola . 1. Find the point where the tangent line intersects the focal axis of the hyperb

A cell phone company has installed three signal towers and at different locations to provide service to their customer

The tyre of a car is of radius 15 inches and it revolves 1000 times in a minute. What is the speed of the car in ? --- B

A batsman hits the ball. The ball attains the maximum height of and drops on the ground at a distance of from the bats

Playing team coaches use parabolic shaped antennas to listen to the conversation between the players in the ground. If t

Man is standing at one focus of a whispering gallery which is 16 feet from the nearest wall. Man is standing at the ot

The orbit of a planet is in elliptical shape with the Sun sitting at one of its two foci. The eccentricity of the ellips

The control towers are located at points and on a straight shore where the -axis runs through. At the same moment both

An architect's design for a building includes some large pillars with cross-sections in the shape of hyperbolas. The cur