If `P S Q` is a focal chord of the parabola `y^2=8x` such that `S P=6` , then the length of `S Q` is (a)6 (b) 4 (c) 3 (d) none of these

If PQ is the focal chord of parabola y=x^(2)-2x+3 such that P-=(2,3) , then find slope of tangent at Q.

The circle x^2+y^2=5 meets the parabola y^2=4x at P and Q . Then the length P Q is equal to (A) 2 (B) 2sqrt(2) (C) 4 (D) none of these

If the length of a focal chord of the parabola y^2=4a x at a distance b from the vertex is c , then prove that b^2c=4a^3dot

Column I, Column II An ellipse passing through the origin has its foci (3, 4) and (6,8). Then the length of its minor axis is, p. 8 If P Q is a focal chord of the ellipse (x^2)/(25)+(y^2)/(16)=1 which passes through S-=(3,0) and P S=2, then the length of chord P Q is, q. 10sqrt(2) If the line y=x+K touches the ellipse 9x^2+16 y^2=144 , then the difference of values of K is, r. 10 The sum of distances of a point on the ellipse (x^2)/9+(y^2)/(16)=1 from the foci is, s. 12

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

If the length of the common chord of two circles x^2+y^2+8x+1=0 and x^2+y^2+2muy-1=0 is 2sqrt(6) , then the values of mu are (a) +-2 (b) +-3 (c) +-4 (d) none of these

The length of focal chord to the parabola y^(2)=12x drawn from the point (3,6) on is __________ .

If S_1a n dS_2 are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and S_3a n dS_4 are the foci of the conjugate hyperbola, then the area of quadrilateral S_1S_3S_2S_4 is 24 (b) 26 (c) 22 (d) none of these

If A B is a focal chord of x^2-2x+y-2=0 whose focus is S and A S=l_1, then find B Sdot

Let PQ be a focal chord of the parabola y^2 = 4ax The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0 . Length of chord PQ is