Class 12

Math

Co-ordinate Geometry

Conic Sections

If three parabols touch all the lines $x=0,y=0$ and $x+y=2$, then maximum area of the triangle formed by joining their foci is

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Find the center, foci, the length of the axes, and the eccentricity of the ellipse $2x_{2}+3y_{2}−4x−12y+13=0$

Find the equation of the circle passing through the points $(4,1)$ and $(6,5)$ and whose centre is on the line $4x+y=16$

Find the center and radius of the circle $x_{2}+y_{2}−4x−8y−45=0$

Find the number of rational points on the ellipse $9x_{2} +4y_{2} =1.$

Prove that any point on the ellipse whose foci are $(−1,0)$ and $(7,0)$ and eccentricity is $21 $ is $(3+8cosθ,43 sinθ),θ∈R˙$

Let $P$ be a point on the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ of eccentricity $e˙$ If $A,A_{′}$ are the vertices and $S,S$ are the foci of the ellipse, then find the ratio area $PSS_{′′}$ : area $APA_{prime}˙$

Find the coordinates of the focus axis of the parabola, the equation of directrix and the length of the latus rectum for the parabola $x_{2}$ $=−16y$.

An ellipse passes through the point $(4,−1)$ and touches the line $x+4y−10=0$ . Find its equation if its axes coincide with the coordinate axes.