For which c does { ( x , y ) : x 2 + y 2 + 2 x − 1 ≤ 0 } ∩ {( x , y ) : x − y + c ≥ 0 } contain exactly one point?

Start Free Mock LoginAlready registered? Login here

Mathematics - Circle Question with Solution | TestHub

MathematicsCircleTangent & NormalMedium2 minQB

MathematicsMediumsingle choice

For which $c$ does ${(x, y) : x^{2} + y^{2} + 2 x - 1 \leq 0} \cap {(x, y) : x - y + c \geq 0}$ contain exactly one point?

Options:

Answer:

Solution:

The disk has centre (-1, 0) and radius $2$ . A tangent line has $∣ - 1 + c ∣/ 2 = 2$ , giving $c = - 1$ or 3. Only for $c = - 1$ is the chosen half-plane outside the disk, leaving its tangent point alone.

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Tangent & Normal

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...