Two straight lines are perpendicular to each other. One of them touches the parabola `y^2=4a(x+a)` and the other touches `y^2=4b(x+b)` . Their point of intersection lies on the line. (a)`x-a+b=0` (b) `x+a-b=0` (c)`x+a+b=0` (d) `x-a-b=0`

The point of intersection of the lines x/a+y/b=1 and x/b+y/a=1 lies on

Let the parabolas y=x(c-x)and y=x^(2)+ax+b touch each other at the point (1,0), then-

The point of intersection of the tangents of the parabola y^2=4x drawn at the endpoints of the chord x+y=2 lies on (a) x-2y=0 (b) x+2y=0 (c) y-x=0 (d) x+y=0

Let the curve C be the mirror image of the parabola y^2 = 4x with respect to the line x+y+4=0 . If A and B are the points of intersection of C with the line y=-5 , then the distance between A and B is

If a + bne 0 , find the coordinates of focus and the length of latus rectum of the parabola y^(2) = 2 mx which passes through the point of intersection of the straight lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 .

The straight lines joining any point P on the parabola y^2=4a x to the vertex and perpendicular from the focus to the tangent at P intersect at Rdot Then the equation of the locus of R is (a) x^2+2y^2-a x=0 (b) 2x^2+y^2-2a x=0 (c) 2x^2+2y^2-a y=0 (d) 2x^2+y^2-2a y=0

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. (a) 3x+y=0 and 3x-y=0 (b) 3x+y=0 and 3y-x=0 (c) x+3y=0 and y-3x=0 (d) x+y=0 and x-y=0

If the parabola y=(a-b)x^2+(b-c)x+(c-a) touches x- axis then the line ax+by+c=0

If the straight line x/a+y/b=1is parallel to the line 4x+3y=6 and passes through the point of intersection of the lines 2x-y-1=0and 3x-4y+6=0,find the values of a and b.

If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b), then the value of a+b is ___________ .