Question

The number of values of 'c' such that the straight line,

$y=4x+c$

touches the curve

$\frac{ {x}^{2} }{4} + {y}^{2} = 1$

is :-

(a) 0

(b) 1

(c) 2

(d) infinite

✔️✔️Proper solution Needed✔️​✔️​

Answer 1

Answer:

Option(c)

Step-by-step explanation:

If 4x + c touches the curve x²/4 + y²/2, then 4x + c must be tangent to curve.

On comparing with y = mx + c,

Slope of the line m = 4.

Now,

For tangency, Δ = 0

a²m² + b² = c²

Given: line is y = 4x + c and curve is x²/4 + y² = 1,

⇒ c² = 4 * 4² + 1

⇒ c² = 64 + 1

⇒ c² = 65

⇒ c = ±65.

Thus, the number of values = 2.

Hope it helps!

Answer 2

Answer:

Step-by-step explanation:

Holla user

Referred the attachment below ⬇️⬇️⬇️⬇️.

Acc to que.

Answer would be 2

All other que were solved by me only.