If `(x/a)+(y/b)=1` and `(x/c)+(y/d)=1` intersect the axes at four concylic points and `a^2+c^2=b^2+d^2,` then these lines can intersect at, `(a , b , c , d >0)` `

If the curves (x^(2))/(a)+(y^(2))/(b)=1 and (x^(2))/(c )+(y^(2))/(d)=1 intersect at right angles then prove that a-b=c-d

(x-1)(y-2)=5 and (x-1)^2+(y+2)^2=r^2 intersect at four points A, B, C, D and if centroid of triangle ABC lies on line y = 3x-4 , then locus of D is

The circle with equation x^2 +y^2 = 1 intersects the line y= 7x+5 at two distinct points A and B. Let C be the point at which the positive x-axis intersects the circle. The angle ACB is

If the ellipse (x^2)/4+y^2=1 meets the ellipse x^2+(y^2)/(a^2)=1 at four distinct points and a=b^2-5b+7, then b does not lie in (a) [4,5] (b) (-oo,2)uu(3,oo) (c) (-oo,0) (d) [2,3]

If a tangent to the parabola y^2 = 4ax intersects the x^2/a^2+y^2/b^2= 1 at A and B , then the locus of the point of intersection of tangents at A and B to the ellipse is

Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0 . Then, (a) C1 and C2 touch each other at one point (b) C1 and C2 touch each other exactly at two point (c) C1 and C2 intersect(but do not touch) at exactly two point (d) C1 and C2 neither intersect nor touch each other

Let C be a curve which is the locus of the point of intersection of lines x=2+m and m y=4-mdot A circle s: (x-2)^2+(y+1)^2=25 intersects the curve C at four points: P ,Q ,R ,a n dS . If O is center of the curve C , then O P^2+O Q^2+O R^2+O S^2 is (a) 50 (b) 100 (c) 25 (d) (25)/2

If a+c = 2b and 2/c= 1/b+1/d then prove that a:b = c:d.

If a , b and c are in A P , then the straight line a x+b y+c=0 will always pass through a fixed point whose coordinates are (a) (1,2) (b) (1,-2) (c) (2,3) (d) (0,0)

A tangent at a point on the circle x^2+y^2=a^2 intersects a concentric circle C at two points Pa n dQ . The tangents to the circle X at Pa n dQ meet at a point on the circle x^2+y^2=b^2dot Then the equation of the circle is (a) x^2+y^2=a b (b) x^2+y^2=(a-b)^2 (c) x^2+y^2=(a+b)^2 (d) x^2+y^2=a^2+b^2