The locus a point P(α,β) moving under the condition that the line y=αx+β is a tangent to the hyperbola a2x2−b2y2=1 is (A) a parabola (B) an ellipse (C) a hyperbola (D) a circle
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XYand XprimeYprimeare two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XYat A and XprimeYprimeat B. Prove that ∠AOB = 90o
Find the locus of the middle point of the portion of the line xcosα+ysinα=p
which is intercepted between the axes, given that p
are the vertices of ABC,
then as α
varies, find the locus of its centroid.
Find the equation of the circle with centre :(21,41) and radius 121
Find the coordinates of the point which divides the line segments joining the points (6,3)
in the ratio 3:2
(i) internally and (ii) externally.
A rod of length l
slides with its ends on two perpendicular lines. Find the locus of its midpoint.
The sum of the squares of the distances of a moving point from two fixed points (a,0) and (−a,0)
is equal to a constant quantity 2c2˙
Find the equation to its locus.
An arch is in the form of a semi–ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.