Tangent to the curve y=x2+6 at a point (1,7) touches the circle x2+y2+16x+12y+c=0at a point Q, then the coordinates of Q are (A) (−6,−11) (B) (−9,−13) (C) (−10,−15) (D) (−6,−7)
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 38m˙
Chords of the ellipse a2x2+b2y2=1 are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the ellipse.
For an ellipse 9x2+4y2=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 OQ2−MQ2
Prove that the chords of contact of pairs of perpendicular tangents to the ellipse a2x2+b2y2=1 touch another fixed ellipse.
If C is the center of the ellipse 9x2+16y2=144 and S is a focus, then find the ratio of CS to the semi-major axis.