Class 11

Math

Co-ordinate Geometry

Conic Sections

If $C$ is the center of the ellipse $9x_{2}+16y_{2}=144$ and $S$ is a focus, then find the ratio of $CS$ to the semi-major axis.

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If from any point $P$ on the circle $x_{2}+y_{2}+2gx+2fy+c=0,$ tangents are drawn to the circle $x_{2}+y_{2}+2gx+2fy+csin_{2}α+(g_{2}+f_{2})cos_{2}α=0$ , then find the angle between the tangents.

Find the equation of the circle having radius 5 and which touches line $3x+4y−11=0$ at point (1, 2).

Perpendiculars are drawn, respectively, from the points $PandQ$ to the chords of contact of the points $QandP$ with respect to a circle. Prove that the ratio of the lengths of perpendiculars is equal to the ratio of the distances of the points $PandQ$ from the center of the circles.

The common chord of the circle $x_{2}+y_{2}+6x+8y−7=0$ and a circle passing through the origin and touching the line $y=x$ always passes through the point. $(−21 ,21 )$ (b) (1, 1) $(21 ,21 )$ (d) none of these

Two circle are externally tangent. Lines $PAB$ and $PA_{′}B_{′}$ are common tangents with $AandA_{′}$ on the smaller circle and $B_{prime}andB_{′}$ the on the larger circle. If $PA=AB=4,$ then the square of the radius of the circle is___________

Tangents are drawn to the circle $x_{2}+y_{2}=a_{2}$ from two points on the axis of $x,$ equidistant from the point $(k,0)˙$ Show that the locus of their intersection is $ky_{2}=a_{2}(k−x)˙$

If the equation $px_{2}+(2−q)xy+3y_{2}−6qx+30y+6q=0$ represents a circle, then find the values of $pandq˙$

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