If the line `y=Kx` is a tangent to `y=e^x` at `P(K!=0)` then the `x`-intercept of normal at `P` to `y=e^(x)` is

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.

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 equation of the tangent to the curve y=1-e^(x//2) at the tangent to the curve y=1-e^(x//2) at the point of intersection with the y-axis, is

If the variable line y=kx+2h is tangent to an ellipse 2x^(2)+3y^(2)=6, then the locus of P(h,k) is a conic C whose eccentricity is 3 . Then the value of 3e^(2) is

If the line x-y-1=0 intersect the parabola y^(2)=8x at P and Q, then find the point on intersection of tangents P and Q.

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) .

A normal is drawn to parabola y^2=4x at (1,2) and tangent is drawn to y=e^x at (c,e^c) . If tangent and normal intersect at x-axis then find C.

If the line (x-y+1)+k(y-2x+4)=0 makes equal intercept on the axes then the value of k is