Correct Answer - Option 1 : y = 4x + 9
CONCEPT:
The slope form of the tangent(s) to the circle x2 + y2 = r2 is given by: \(y = mx ± r ⋅ √{1 + m^2}\)
CALCULATION:
Given: Equation of circle is x2 + y2 = 9 and slope of tangent is √8
Here, m = √8 and r = 3
As we know that, the equation of tangent in the slope form to the circle x2 + y2 = r2 is given by:\(y = mx ± r ⋅ √{1 + m^2}\)
⇒ \(\rm y = 4⋅ x ± 3 ⋅ √{1 + ({√ 8)}^2}\)
So, the required equation of tangent(s) to the circle are: y = 4x ± 3⋅3
y = 4x ± 9
Hence, option A is the correct answer.
