Class 12

Math

Co-ordinate Geometry

Ellipse

Coordinates of the vertices B and C of a triangle ABC are (2,0) and (8,0) respectively. The vertex A is varying in such a way that $4tan.2B .tan.2C =1$. Then locus of A is

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

If the normal at any point P on the ellipse cuts the major and mirror axes in G and g respectively and C be the centre of the ellipse, then

If the normal at any point P on ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ meets the auxiliary circle at Q and R such that $∠QOR=90_{∘}$ where O is centre of ellipse, then

Let $Q=(3,5 ),R=(7,35 )$. A point P in the XY-plane varies in such a way that perimeter of $ΔPQR$ is 16. Then the maximum area of $ΔPQR$ is

If the normal at one end of the latus rectum of the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ passes through one end of the minor axis, then prove that ecentricitty is constant.

An equilateral triangle is inscribed in an ellipse whose equation is $x_{2}+4y_{2}=4$. If one vertex of the triangle is (0,1) then the length of each side is

The mormal at point $P(2,233 )$ on the ellipse $16x_{2} +9y_{2} =1$ meets the major axis of the ellipse at Q. If S and S are foci of given ellipe, then the rartio $SQ:SQ$

The foci of an ellise are S(3,1) and S' (11,5). If the normal at is P is x+2y-15=0, then find the coordinattes of point P.

If the length of the major axis intercepted between the tangent and normal at a point $P(acosθ,bsinθ)$ on the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ is equal to the length of semi-major axis, then eccentricity of the ellipse is