The number of values of 'c' such that the line y = 4x + c touches the curve (x2/4)+y2=1

Question

The number of values of 'c' such that the line y = 4x + c touches the curve (x2/4)+y2=1 (A) 0 (B) 1 (C) 2 (D) infinite

Tardigrade Admin · Accepted Answer

Given, y=4 x+c and (x2/4)+y2=1 Condition for tangency, c2=a2 m2+b2 ∴ c2=4(4)2+12 ⇒ c2 =65 ⇒ c=± √65 Hence, for two values of c, the line touches the curve.

Q. The number of values of $^{'} c^{'}$ such that the line $y = 4 x + c$ touches the curve $\frac{x ^{2}}{4} + y^{2} = 1$

0

1

2

infinite

Given, $y = 4 x + c$ and $\frac{x ^{2}}{4} + y^{2} = 1$
Condition for tangency,
$c^{2} = a^{2} m^{2} + b^{2}$
$∴ c^{2} = 4 (4)^{2} + 1^{2}$
$\Rightarrow c^{2} = 65$
$\Rightarrow c = \pm 65$
Hence, for two values of $c$ , the line touches the curve.

Q. The number of values of ′c′ such that the line y=4x+c touches the curve 4x2​+y2=1

0

1

2

infinite

Given, y=4x+c and 4x2​+y2=1 Condition for tangency, c2=a2m2+b2 ∴c2=4(4)2+12 ⇒c2=65 ⇒c=±65​ Hence, for two values of c, the line touches the curve.

Q. The number of values of $^{'} c^{'}$ such that the line $y = 4 x + c$ touches the curve $\frac{x ^{2}}{4} + y^{2} = 1$

Given, $y = 4 x + c$ and $\frac{x ^{2}}{4} + y^{2} = 1$
Condition for tangency,
$c^{2} = a^{2} m^{2} + b^{2}$
$∴ c^{2} = 4 (4)^{2} + 1^{2}$
$\Rightarrow c^{2} = 65$
$\Rightarrow c = \pm 65$
Hence, for two values of $c$ , the line touches the curve.