Question

The equations of tangents drawn from the point (2,3) to the ellipse $9x^2+16y^2=144$ are:

• A. $y=3$
• B. $y=5$
• C. $y=-x+3$
• D. $y=-x+5$

Answer 1

Answer: (A), (D)

$y=-x+5$

the slope form of tangent to the given ellipse is:
$y=mx\pm 16m^2+9$
Also, it passes through (2,3)
$\therefore 3=2m+\sqrt{16m^2+9}\Rightarrow (3-2m{)}^2=16m^2+9\Rightarrow 12m^2+12m=0\Rightarrow m=0,-1$
Hence, the equation of the tangents are:
y = 3 and y = -x + 5