Point of contact when line `y=mx+c` touches the hyperbola

Find the condition that the straight line y = mx + c touches the hyperbola x^(2) - y^(2) = a^(2) .

Find the condition that the straight line y = mx + c touches the hyperbola x^(2) - y^(2) = a^(2) .

Find the range of c for which the line y=mx+ c touches the parabola y^(2)=8(x+2)

The coordinates of the point of contact of the straight line y=mx+c to the parabola y^(2)=4ax is

Prove that the line x + y + 2 = 0 touches the hyperbola 3x^2 - 5y^2 = 30 and find the point of contact. Find also the equation of normal at the point.

If the values of m for which the line y= mx +2sqrt5 touches the hyperbola 16x^2 — 9y^2 =144 are the roots of the equation x^2 -(a +b)x-4 = 0 , then the value of a+b is

Prove that the line 5x+12y=9 touches the hyperbola x^(2)-9y^(2)=9 and find the point of contact.

Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = (a)/(m) .

If the values of m for which the line y=mx+2sqrt(5) touches the hyperbola 16x^(2)-9y^(2)=144 are the roots of the equation x^(2)-(a+b)x-4=0 , then the value of a+b is