Class 11

Math

Co-ordinate Geometry

Conic Sections

If $ax +by =2 $ touches the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ , then find the eccentric angle $θ$ of point of contact.

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Consider the circles $x_{2}+(y−1)_{2}=9,(x−1)_{2}+y_{2}=25.$ They are such that these circles touch each other one of these circles lies entirely inside the other each of these circles lies outside the other they intersect at two points.

Find the equations of tangents to the circle $x_{2}+y_{2}−22x−4y+25=0$ which are perpendicular to the line $5x+12y+8=0$

Find the length of the tangent drawn from any point on the circle $x_{2}+y_{2}+2gx+2fy+c_{1}=0$ to the circle $x_{2}+y_{2}+2gx+2fy+c_{2}=0$

If a circle passes through the point $(0,0),(a,0)and(0,b)$ , then find its center.

Find the image of the circle $x_{2}+y_{2}−2x+4y−4=0$ in the line $2x−3y+5=0$

The line $9x+y−18=0$ is the chord of contact of the point $P(h,k)$ with respect to the circle $2x_{2}+2y_{2}−3x+5y−7=0$ , for (a)$(524 ,−54 )$ (b) $P(3,1)$ (c)$P(−3,1)$ (d) $(−52 ,512 )$

If the abscissa and ordinates of two points $PandQ$ are the roots of the equations $x_{2}+2ax−b_{2}=0$ and $x_{2}+2px−q_{2}=0$ , respectively, then find the equation of the circle with $PQ$ as diameter.

If the chord of contact of the tangents drawn from the point $(h,k)$ to the circle $x_{2}+y_{2}=a_{2}$ subtends a right angle at the center, then prove that $h_{2}+k_{2}=2a_{2}˙$