class 11

Math

Co-ordinate Geometry

Conic Sections

Let PQ be a focal chord of the parabola $y_{2}=4ax$ The tangents to the parabola at P and Q meet at a point lying on the line $y=2x+a,a>0$. Length of chord PQ is

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Two circles are given such that one is completely lying inside the other without touching. Prove that the locus of the center of variable circle which touches the smaller circle from outside and the bigger circle from inside is an ellipse.

Find the equation of the circle with centre $(0,2)$ and radius $2$

Find the equation of the circle with centre $(−a,−b)$ and radius $a_{2}−b_{2} $

Find the equation of the circle with centre $(1,1)$ and radius $2 $

Find the point on the hyperbola $x_{2}−9y_{2}=9$ where the line $5x+12y=9$ touches it.

Find the equation of the chord of the hyperbola $25x_{2}−16y_{2}=400$ which is bisected at the point (5, 3).

Find the foci of the ellipse $25(x+1)_{2}+9(y+2)_{2}=225.$

If (5, 12) and (24, 7) are the foci of an ellipse passing through the origin, then find the eccentricity of the ellipse.