Class 10

Math

All topics

Conic Sections

AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then the length of AP (in cm) is

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $4x_{2}+9y_{2}=36$

If the tangent at any point of the ellipse $a_{3}x_{2} +b_{2}y_{2} =1$ makes an angle $α$ with the major axis and an angle $β$ with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by $e=cosαcosβ $

Find the coordinates of the foci, the vertices the eccentricity and the length of latus rectum of the hyperbola $16x_{2}−9y_{2}=576$

Find the equation of the circle passing through the points $(2,3)$ and $(−1,1)$ and whose centre is on the line $x−3y−11=0$

Find the angle between the asymptotes of the hyperbola $16x_{2} −9y_{2} =1$ .

Find the slope of a common tangent to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ and a concentric circle of radius $r˙$

P is the point on the ellipse is$16x_{2} +9y_{2} =1andQ$ is the corresponding point on the auxiliary circle of the ellipse. If the line joining the center C to Q meets the normal at P with respect to the given ellipse at K, then find the value of CK.

$O$is the origin & also the centre of two concentric circles having radii of the inner & the outer circle as \displaystyle{a}&{b} respectively. A line $OPQ$ is drawn to cut the inner circle in $P$ & the outer circle in $Q.PR$ is drawn parallel to the $y$-axis & $QR$ is drawn parallel to the $x$-axis. Prove that the locus of $R$ is an ellipse touching the two circles. If the focii of this ellipse lie on the inner circle, find the ratio of inner: outer radii & find also the eccentricity of the ellipse.