Generate Quiz 686BBE02A8A5A

C is the right response.

The length of a hyperbola’s transverse axis is equal to the difference between its focal distances at any given position. [Derivation is available online at locations such as BYJU’S.]

We may observe that the term with x^2 is positive and the term with y^2 is negative in the provided equation. This indicates that the x-axis is parallel to the transverse axis.

Since 4 is the square root of 16, 2a = 4 is the transverse axis’s length. Consequently, a = 2.

The response is (c) 8.

This is the right formula for the equation of tangents to a circle that are parallel to the line y = mx + b, which is x² + y² = a². Two tangent lines with the same slope (m) but opposite signs in the ± term can be drawn to the circle, as indicated by the ± symbol.

In conclusion, the proper equation for tangents to a circle x² + y² = a² that are parallel to the line y = mx + b is y = mx ± a√(1 + m²). This formula calculates the equations of the two tangent lines by taking into account the radius (a) of the circle and the slope (m) of the parallel line.