Let A(6,4)andB(2,12) be two given point. Find the slope of a line perpendicular to AB˙
Find the equation of the circle passing through the points (2,3)and (−1,1)and whose centre is on the line x−3y−11=0.
The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Find the coordinates of the circumcenter of the triangle whose vertices are (A(5,−1),B(−1,5), and C(6,6)˙ Find its radius also.
The coordinates of the point AandB are (a,0) and (−a,0), respectively. If a point P moves so that PA2−PB2=2k2, when k is constant, then find the equation to the locus of the point P˙
Given the equation 4x2+23xy+2y2=1 . Through what angle should the axes be rotated so that the term xy is removed from the transformed equation.
If two equal chords of a circle intersect within the circle, prove that the linejoining the point of intersection to the centre makes equal angles with the chords.