Home
Class 12
MATHS
Find the condition that the straight lin...

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

Text Solution

Verified by Experts

The correct Answer is:
`c^(2) = a^(2)(m^(2)-1)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The line y = 4x + c touches the hyperbola x^(2) - y^(2) = 1 if

Find the conditions that the line (i) y = mx + c may touch the circle x^(2) +y^(2) = a^(2) , (ii) y = mx + c may touch the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 .

The line y=mx+2 touches the hyperola 4x^(2)-9y^(2)=36 then m=

Show that the line y =x + sqrt7 touches the hyperbola 9x ^(2) - 16 y ^(2) = 144.

The straight line x+y= k touches the parabola y=x-x^(2) then k =

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

The line y=x+2 touches the hyperbola 5x^2-9y^2=45 at the point

Find the condition that line lx + my - n = 0 will be a normal to the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 .

The straight-line y= mx+ c cuts the circle x^(2) + y^(2) = a^(2) in real points if :

If the line y=mx+c touches the parabola y^(2)=4a(x+a) , then