Find the equations of tangents to the ellipse
x225+y216=1
which are parallel to 3x+2y=25
3x + 2y = 17
3x + 2y + 17 = 0
Any line parallel to 3x + 2y = 25 can be written as 3x + 2y = k
We want to find the value of k. We can re - arrange
3x + 2y = k as y=−32x+k2
Equation of tangent with Slope m to the ellipse
x2a2+y2b2=1 is given by y=mx∓√a2m2+b2
Here
m=−32 ⇒ k2=∓√25×(−32)2+16
⇒ k2=∓√(5×32)2+16
=∓√225+644
=∓√2894
=∓172
⇒ k=∓17
So the equation of tangents are 3x + 2y = 17 and 3x + 2y + 17 = 0