Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to
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If two equal chords of a circle intersect within the circle, prove that the segments ofone chord are equal to corresponding segments of the other chord.
The equation of curve referred to the new axes, axes retaining their directions, and origin (4,5)
. Find the equation referred to the original axes.
Find the equations of the hyperbola satisfying the given conditions :Foci (±35,0), the latus rectum is of length 8.
Find an equation of the circle with centre at (0,0) and radius r.
Find the equation of the parabola that satisfies the given conditions:Vertex (0, 0); focus (3,0)
Determine x so that the line passing through (3,4)and(x,5) makes an angle of 1350 with the positive direction of the x-axis.
internally in the ratio λ1:λ2
externally in the ratio λ1;λ2,
then prove that OA
is the harmonic mean of OP
Find the equation for the ellipse that satisfies the given conditions:Foci (±3,0),a=4