If the radius of the circle touching the pair of lines 7x2−18xy+7y2=0 and the circle x2+y2−8x−8y=0, and contained in the given circle is equal to k, then k2 is equal to
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Find the equation for the ellipse that satisfies the given conditions: Foci (±3,0),a=4.
Prove that the chord of contact of the ellipse a2x2+b2y2=1
with respect to any point on the directrix is a focal chord.
Find the locus of point P
such that the tangents drawn from it to the given ellipse a2x2+b2y2=1
meet the coordinate axes at concyclic points.
If two points are taken on the minor axis of an ellipse a2x2+b2y2=1
at the same distance from the center as the foci, then prove that the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is 2a2˙
Find the equation of the curve whose parametric equation are x=1+4cosθ,y=2+3sinθ,θ∈R˙
Find the maximum area of the ellipse a2x2+b2y2=1
which touches the line y=3x+2.
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 36x2+4y2=144
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˙