If two chords of circle `x^2+y^2-a x-b y=0` , drawn from the point (a, b) is divided by the x-axis in the ratio 2: 1 then : `a^2>3b^2` (b) `a^2<3b^2` (c) `a^2>4b^2` (d) `a^2<4b^2`

If two distnct chords of the circle x^2+y^2 -2x -4y=0 drawn from the point P (a,b) are bisected by y-axis then a) (b+2)^2>4a b) (b-2)^2>4a c) (b-2)^2>2a d) (b+2)^2>a

The locus of the midpoints of the chords of the circle x^2+y^2-a x-b y=0 which subtend a right angle at (a/2, b/2) is (a) a x+b y=0 (b) a x+b y=a^2+b^2 (c) x^2+y^2-a x-b y+(a^2+b^2)/8=0 (d) x^2+y^2-a x-b y-(a^2+b^2)/8=0

If two distinct chords drawn from the point (a, b) on the circle x^2+y^2-ax-by=0 (where ab!=0) are bisected by the x-axis, then the roots of the quadratic equation bx^2 - ax + 2b = 0 are necessarily. (A) imaginary (B) real and equal (C) real and unequal (D) rational

If two distinct chords, drawn from the point (p, q) on the circle x^2+y^2=p x+q y (where p q!=q) are bisected by the x-axis, then p^2=q^2 (b) p^2=8q^2 p^2 8q^2

If two distinct chords, drawn from the point (p, q) on the circle x^2+y^2=p x+q y (where p q!=q) are bisected by the x-axis, then p^2=q^2 (b) p^2=8q^2 p^2 8q^2

A given line L_1 cut x and y-axes at P and Q respectively and has intercepts a and b/2 on x and y-axes respectively. Let another line L_2 perpendicular to L_1 cut x and y-axes at R and S respectively. Let T be the point of intersection of PS and QR . If two chords each bisected by x-axis can be drawn from (a, b/2) to the locus of T , then (A) a^2 gt 2b^2 (B) b^2 gt 2a^2 (C) a^2 lt 2b^2 (D) b^2 lt 2a^2

The equations of tangents to the circle x^2+y^2-6x-6y+9=0 drawn from the origin in (a). x=0 (b) x=y (c) y=0 (d) x+y=0

A variable chord of the circle x^2+y^2=4 is drawn from the point P(3,5) meeting the circle at the point A and Bdot A point Q is taken on the chord such that 2P Q=P A+P B . The locus of Q is x^2+y^2+3x+4y=0 x^2+y^2=36 x^2+y^2=16 x^2+y^2-3x-5y=0

The distance of point P(x, y) from the points A(1, -3) and B(-2, 2) are in the ratio 2 : 3. Show that 5x^(2) + 5y^(2) - 34x + 70y + 58 = 0 .

The tangents drawn from origin to the circle x^2+y^2-2ax-2by+b^2 are perpendicular to each other, if a) a-b =1 b) a+b=1 c) a^2-b^2 =0 d) a^2+b^2=1