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>2b^2` (b) `a^2<3b^2` `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)>4ab)(b-2)^(2)>4ac)(b-2)^(2)>2ad)(b+2)^(2)>a

Two chords are drawn from the point P(h,k) on the circle x^(2)+y^(2)=hx+ky. If the y-axis divides both the chords in the ratio 2:3, then

The center of circle x^2+y^2-6x+4y-12=0 is (a,b) then (2a + 3b) is

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

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

A point (-4,1) divides the line joining A(2,-2) and B(x,y) in the ratio 3:5. Then point B is

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

The circle x^(2)+y^(2)-2x+5y-24=0 cuts the x -axis at A and B and y -axis at C and D then AB+CD=

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

If two distinct chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=2 can be drawn through the point (a-b) .each bisectde by the line x+y=b then the least integral value ((a)/(b))^(2)+6((a)/(b)) can take is equal to