Let O be the vertex and Q be any point on the parabola,x2=8y. It the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :
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The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.
Find the equation of a circle with centre (2,2) and passes through the point (4,5).
Find the equation of the circle with centre (−2,3) and radius 4
Find the center and radius of the circle x2+y2−4x−8y−45=0
Find the equation for the ellipse that satisfies the given conditions:
If the tangent at any point of the ellipse a3x2+b2y2=1
makes an angle α
with the major axis and an angle β
with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosαcosβ
Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse a2x2+b2y2=1.
Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (±3,0) ends of minor axis (0,±2).