class 11

Math

Co-ordinate Geometry

Conic Sections

Tangent to the curve $y=x_{2}+6$ at a point $(1,7)$ touches the circle $x_{2}+y_{2}+16x+12y+c=0$at a point $Q$, then the coordinates of $Q$ are (A) $(−6,−11)$ (B) $(−9,−13)$ (C) $(−10,−15)$ (D) $(−6,−7)$

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An arc of a bridge is semi-elliptical with the major axis horizontal. If the length of the base is 9m and the highest part of the bridge is 3m from the horizontal, then prove that the best approximation of the height of the acr 2 m from the center of the base is $38 m˙$

Chords of the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the ellipse.

For an ellipse $9x_{2} +4y_{2} =1$ with vertices A and A', drawn at the point P in the first quadrant meets the y axis in Q and the chord A'P meets the y axis in M. If 'O' is the origin then $OQ_{2}−MQ_{2}$

Prove that the chords of contact of pairs of perpendicular tangents to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ touch another fixed ellipse.

Two perpendicular tangents drawn to the ellipse $25x_{2} +16y_{2} =1$ intersect on the curve.

Find the eccentric angles of the extremities of the latus recta of the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$

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.

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