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If the tangents on the ellipse 4x2 + y2 = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a2 is equal to

(a)

 

(b)

 

(c)

 

(d)

 


Question ID - 57535 | Toppr Answer

If the tangents on the ellipse 4x2 + y2 = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a2 is equal to

(a)

 

(b)

 

(c)

 

(d)

 

1 Answer - 5876 Votes

3537

Answer Key : (b) -

Equation of tangent at A(1, 2);

4x + 2y = 8 ⇒ 2x + y = 4

So tangent at B(a, b) can be assumed as

x − 2y = c    ⇒    y =

Condition for tangency

 

Equation of tangent;  x − 2y =      ...(i)

Equation of tangent at P(a, b); 4ax + by = 8...(ii)

Comparing both the equations;

 

⇒ a = 2

⇒ a2 =



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