# If Y – 2x – K = 0 Touches the Conic 3x2 – 5y2 = 15, Find the Value of K. - Mathematics

Sum

If y – 2x – k = 0 touches the conic 3x2 – 5y2 = 15, find the value of k.

#### Solution

Given line is y - 2x - k = 0

or y = 2x + k

Given conic section is 3x2 - 5y2 = 15

or "x"^2/5 - "y"^2/3 = 1

Here, m = 2, a2 = 5 and b2 = 3

Line y = mx + c touches the conic section

"x"^2/"a"^2 - "y"^2/"b"^2 = 1 (Hyperbola)

"y" = "mx"+- sqrt("a"^2"m"^2 - "b"^2)

"2x + "k" = 2"x" +- sqrt (5(2)^2 - 3)

"k" = +-sqrt(20-3)

k = +-sqrt17

Concept: Equation of a Line in Space
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