If `O Aa n dO B` are equal perpendicular chords of the circles `x^2+y^2-2x+4y=0` , then the equations of `O Aa n dO B` are, where `O` is the origin.

If 2 x-3 y=0 is the equation of the common chord of the circles, x^2+y^2+4 x=0 and x^2+y^2+2 lambda y=0 , then the value of lambda is

If O is the origin and O Pa n dO Q are the tangents from the origin to the circle x^2+y^2-6x+4y+8=0 , then the circumcenter of triangle O P Q is (3,-2) (b) (3/2,-1) (c) (3/4,-1/2) (d) (-3/2,1)

If aa n dc are the lengths of segments of any focal chord of the parabola y^2=2b x ,(b >0), then the roots of the equation a x^2+b x+c=0 are (a)real and distinct (b) real and equal (c)imaginary (d) none of these

If points Aa n dB are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is (a) x^2+y^2=4 (b) x^2+y^2-x-y=0 (c) x^2+y^2-2x-2y+1=0 (d) x^2+y^2+2x-2y+1=0

The equation of the chord of the circle x^2+y^2-3x-4y-4=0 , which passes through the origin such that the origin divides it in the ratio 4:1, is

If the circle x^2+y^2+2x+3y+1=0 cuts x^2+y^2+4x+3y+2=0 at Aa n dB , then find the equation of the circle on A B as diameter.

A line is drawn perpendicular to line y=5x , meeting the coordinate axes at Aa n dB . If the area of triangle O A B is 10 sq. units, where O is the origin, then the equation of drawn line is (a) 3x-y-9 (b) 5y+x=10 (c) 5y+x=-10 (d) x-4y=10

If a circle of radius r is touching the lines x^2-4x y+y^2=0 in the first quadrant at points Aa n dB , then the area of triangle O A B(O being the origin) is (a) 3sqrt(3)(r^2)/4 (b) (sqrt(3)r^2)/4 (c) (3r^2)/4 (d) r^2

If Q is a point on the locus of x^(2)+y^(2)+4x-3y+7=0 , then find the equation of locus of P which divides segment OQ externally in the ratio 3:4, where O is origin.

If Q is a point on the locus of x^(2) + y^(2) + 4x - 3y +7=0 , then find the equation of locus of P which divides segment OQ externally in the ratio 3:4, where O is the origin.