The lines `3x+4y=9&4x-3y+12=0` intersect at `Pdot` The first line intersects `x-a xi s` at `A` and the second line intersects `y-a xi s` at `Bdot` Then the circumradius of the triangle `P A B` is `3/2` (b) `5/2` (c) 10 (d) none

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

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

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at Aa n dB , 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

The line 2x+y=3 intersects the ellipse 4x^(2)+y^(2)=5 at two points. The point of intersection of the tangents to the ellipse at these point is

Let the line y = mx intersects the curve y^2 = x at P and tangent to y^2 = x at P intersects x-axis at Q. If area ( triangle OPQ) = 4, find m (m gt 0) .

Let the line y = mx intersects the curve y^2 = x at P and tangent to y^2 = x at P intersects x-axis at Q. If area ( triangle OPQ) = 4, find m (m gt 0) .

The line through (4, 3) and (-6, 0) intersects the line 5x+y=0 . Find the angles of intersection.

Show that the two lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-4)/5=(y-1)/2=z intersect. Find also the point of intersection of these lines.

The line x-y=1 intersects the parabola y^2=4x at A and B . Normals at Aa n dB intersect at Cdot If D is the point at which line C D is normal to the parabola, then the coordinates of D are (4,-4) (b) (4,4) (-4,-4) (d) none of these

The direction ratios of the line of intersection of the planes x-y+z+3 =0 and x-3y -5 =0 are