Two different non-parallel lines meet the circle `abs(z)=r`. One of them at points a and b and the other which is tangent to the circle at c. Show that the point of intersection of two lines is `(2c^(-1)-a^(-1)-b^(-1))/(c^(-2)-a^(-1)b^(-1))`.

Equation of the tangent to the circle at the point (1, -1) whose centre is the point of intersection of the straight lines x-y=1 and 2x+y-3=0, is

Two different non-parallel lines cut the circle |z| = r at points a, b, c and d , respectively. Prove that these lines meet at the point z given by (a^-1+b^-1-c^-1-d^-1)/(a^-1b^-1-c^-1d^-1)

If the two intersecting lines intersect the hyperbola and neither of them is a tangent to it, then the number of intersecting points are (a)1 (b) 2 (c) 3 (d) 4

The line y=mx+c intersects the circle x^(2)+y^(2)=r^(2) in two distinct points if

If a and b are position vector of two points A,B and C divides AB in ratio 2:1, then position vector of C is

For a> b>c>0 , if the distance between (1,1) and the point of intersection of the line ax+by-c=0 is less than 2sqrt2 then,

Two circles intersect each other at points A and B. A straight line PAQ cuts the circles at P and Q. If the tangents at P and Q intersect at point T, show that the points P, B, Q and T are concylic.

There are two perpendicular lines, one touches to the circle x^(2) + y^(2) = r_(1)^(2) and other touches to the circle x^(2) + y^(2) = r_(2)^(2) if the locus of the point of intersection of these tangents is x^(2) + y^(2) = 9 , then the value of r_(1)^(2) + r_(2)^(2) is.

Three points represented by the complex numbers a,b,c lie on a circle with centre 0 and rdius r. The tangent at C cuts the chord joining the points a,b and z. Show that z= (a^-1+b^-1-2c^-1)/(a^-1b^-1-c^-2)

Assertion: If each of m points on one straight line be joined to each of n points on the other straight line terminated by the points, then number of points of intersection of these lines excluding the points on the given lines is (mn(m-1)(n-1))/2 Reason: Two points on one line and two points on other line gives one such point of intersection. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.