A circle S passes through the point (0, 1) and is orthogonal to the circles (x−1)2+y2=16 and x2+y2=1. Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)
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Prove that the area of the triangle whose vertices are (t,t−2),(t+2,t+2),
is independent of t˙
An equilateral triangle is inscribed in the parabola y2=4ax where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.
A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.
Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas:(i) 9x2−16y2=1 (ii) y2−16x2=1
The points (−a,−b),(a,b),(a2,ab)
(a) vertices of an equilateral triangle
(b) vertices of a right angled triangle
(c) vertices of an isosceles triangle
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is(A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm
In any triangle ABC, if the angle bisector of ∠Aand perpendicular bisector of BCintersect, prove that they intersect on the circumcircle of the triangle ABC
If (xi,yi),i=1,2,3, are the vertices of an equilateral triangle such that (x1+2)2+(y1−3)2=(x2+2)2+(y2−3)2=(x3+2)2+(y3−3)2, then find the value of y1+y2+y3x1+x2+x3 .