Question

find the equation of tangents and normal to the ellipse x² +8y2 = 33 at (-1,2).
iven ellipse equation is x² +8y2 = 33 and point (-1,2)​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer :-

x - 16y + 33 = 0

6x + y + 14 = 0.

Step-by-step explanation :-

Given :-

Ellipse is x² + 8y² = 33

Point is p(x₁,y₁) = (-1,2)

To find :-

Equation of tangent.

Equation of the normal.

Solution :-

The equation of tangent at p(-1,2) is

xy₁ + 8yy₁ = 33

x(-1) + 8y(2) = 33

x - 16y + 33 = 0

Equation of the normal is 16x + y + k = 0

But it passes through p(-1,2)

16(-1) + 2 + k = 0

k = 14

∴ Normal is 16x + y + 14 = 0.