The equation of a line parallel to the line 3x + 4y = 0 and touching the circle x2 + y2 = 9 in the first quadrant is

Question

The equation of a line parallel to the line 3x + 4y = 0 and touching the circle x2 + y2 = 9 in the first quadrant is (A) 3x + 4y = 15 (B) 3x + 4y = 45 (C) 3x + 4y = 9 (D) 3x + 4y = 27

Tardigrade Admin · Accepted Answer

Let, the equation be 3x + 4y = k then, y=- (3/4)x+(k/4). By condition of tangency ((k/4))2=9(1+((-3/4))2) ⇒ k =± 15 3x + 4y = 15 touches in the first quadrant.

Q. The equation of a line parallel to the line $3 x + 4 y = 0$ and touching the circle $x^{2} + y^{2} = 9$ in the first quadrant is

$3 x + 4 y = 15$

$3 x + 4 y = 45$

$3 x + 4 y = 9$

$3 x + 4 y = 27$

Let, the equation be $3 x + 4 y = k$
then, $y = - \frac{3}{4} x + \frac{k}{4}$ . By condition of tangency $(\frac{k}{4})^{2} = 9 (1 + (\frac{- 3}{4})^{2}) \Rightarrow k = \pm 15$
$3 x + 4 y = 15$ touches in the first quadrant.

Q. The equation of a line parallel to the line 3x+4y=0 and touching the circle x2+y2=9 in the first quadrant is

3x+4y=15

3x+4y=45

3x+4y=9

3x+4y=27