The equation of common tangent to the curves y2=20 x and (x2/25)+(y2/120)=1 having positive gradient is

Question

The equation of common tangent to the curves y2=20 x and (x2/25)+(y2/120)=1 having positive gradient is (A) √5 y=x+25 (B) √5 y=x-25 (C) √5 y=x+5 (D) √5 y=x-5

Tardigrade Admin · Accepted Answer

y = mx +(5/ m )( m >0) ....(1) ∴ (25/ m 2)=25 m 2+120 text (using condition of tangency) ⇒ m =(1/√5)

Q. The equation of common tangent to the curves $y^{2} = 20 x$ and $\frac{x ^{2}}{25} + \frac{y ^{2}}{120} = 1$ having positive gradient is

$5 y = x + 25$

$5 y = x - 25$

$5 y = x + 5$

$5 y = x - 5$

$y = m x + \frac{5}{m} (m > 0)$ ....(1)
$∴ \frac{25}{m ^{2}} = 25 m^{2} + 120 (using condition of tangency) \Rightarrow m = \frac{1}{5}$

Q. The equation of common tangent to the curves y2=20x and 25x2​+120y2​=1 having positive gradient is

5​y=x+25

5​y=x−25

5​y=x+5

5​y=x−5