the equations of the tangents to `9x^2+16y^2=144 ,` which make equal intercepts on the coordinate axes.

Options

A. x + y = 5
B. x + y = 16
C. x + y = 15
D. None of these

Answer

A

Explanation

Given curve is `9x^(2) + 16y^(2) = 144`
`implies (x^(2))/(16) + (y^(2))/(9) = 1 `
Let the equation of tangent is x + y = k
`implies y = -x + k`
It is a tangent to the given curve if
`c^(2) = a^(2) m^(2) + b^(2)`
`implies k^(2) = 16(-1)^(2) + 9`
`implies k^(2) = 25`
`implies k = pm 5`
`therefore` Required equation of tangent are
`x + y = pm5`