From any point `P` lying in the first quadrant on the ellipse `(x^2)/(25)+(y^2)/(16)=1,P N` is drawn perpendicular to the major axis and produced at `Q` so that `N Q` equals to `P S ,` where `S` is a focus. Then the locus of `Q` is (a) `5y-3x-25=0` (b) `3x+5y+25=0` (c)`3x-5y-25=0` (d) none of these

Find the equation of a chord of the ellipse (x^2)/(25)+(y^2)/(16)=1 joining two points P(pi/4) and Q((5pi)/4)

The lines p(p^2+1)x-y+q=0 and (p^2+1)^2x+(p^2+1)y+2q=0 are perpendicular to a common line for

If from a point P , tangents P Qa n dP R are drawn to the ellipse (x^2)/2+y^2=1 so that the equation of Q R is x+3y=1, then find the coordinates of Pdot

Tangent drawn from the point (a ,3) to the circle 2x^2+2y^2=25 will be perpendicular to each other if a equals a)5 (b) -4 (c) 4 (d) -5

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

The locus fo the center of the circles such that the point (2, 3) is the midpoint of the chord 5x+2y=16 is (a) 2x-5y+11=0 (b) 2x+5y-11=0 (c) 2x+5y+11=0 (d) none of these

If the mid-point of a chord of the ellipse (x^2)/(16)+(y^2)/(25)=1 (0, 3), then length of the chord is (1) (32)/5 (2) 16 (3) 4/5 (4)12 (5) 32

If the normal to the ellipse 3x^(2)+4y^(2)=12 at a point P on it is parallel to the line , 2x+y=4 and the tangent to the ellipse at P passes through Q (4,4) then Pq is equal to

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at A and B , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is (a) 3x-4y+2=0 (b) 4x+3y+7=0 (c) 6x-8y+7=0 (d) none of these

If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)/(16)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of hyperbola is (x^2)/9-(y^2)/(16)=1 b. the equation of hyperbola is (x^2)/9-(y^2)/(25)=1 c. focus of hyperbola is (5, 0) d. focus of hyperbola is (5sqrt(3),0)