Application of DerivativeHard
Question
On the ellipse 4x2 + 9y2 = 1, the point at which the tangents are parallel to the line 8x = 9y, are
Options
A.
B.
C.
D.
Solution
Given, 4x2 + 9y2 = 1 .....(i)
8x + 18y
= 0
⇒
The tangent at point (h, k) will be parallel to 8x = 9y, then
⇒ h = -2k
Point (h, k) also lies on the ellipse.
∴ 4h2 + 9k2 = 1 .....(ii)
On putting value of h in Eq. (ii), we get
4(-2k)2 + 9k2 = 1
⇒ 16k2 + 9k2 = 1
⇒ 25k2 = 1 ⇒ k2 =
⇒ k
Thus, the point wher the tangents are parallel to 8x = 9y are
and 
Therefore, (b) and (d) are the answers.
8x + 18y
= 0⇒
The tangent at point (h, k) will be parallel to 8x = 9y, then
⇒ h = -2k
Point (h, k) also lies on the ellipse.
∴ 4h2 + 9k2 = 1 .....(ii)
On putting value of h in Eq. (ii), we get
4(-2k)2 + 9k2 = 1
⇒ 16k2 + 9k2 = 1
⇒ 25k2 = 1 ⇒ k2 =
⇒ k
Thus, the point wher the tangents are parallel to 8x = 9y are
and Therefore, (b) and (d) are the answers.
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