AP EAMCET · Maths · Circle
If the angle between the tangents drawn to the circle \(x^2+y^2-12 x-16 y=0\) at the points where the line \(5 y=5 x+k\) cut the circle is \(60^{\circ}\), then the value of \(k\) is
- A \(5+\sqrt{2}\)
- B \(5(2 \pm 5 \sqrt{2})\)
- C \(2 \pm 5 \sqrt{2}\)
- D \(5 \pm 5 \sqrt{2}\)
Answer & Solution
Correct Answer
(B) \(5(2 \pm 5 \sqrt{2})\)
Step-by-step Solution
Detailed explanation
Let the point \(P\left(x_1, y_1\right)\), then \[ \frac{10}{\sqrt{x_1^2+y_1^2-12 x_1-16 y_1}}=\frac{1}{\sqrt{3}} \] \(\Rightarrow \quad x_1^2+y_1^2-12 x_1-16 y_1=300\) Since, line \(A B, 5 y=5 x+k\), is a chord of contact of circle with respect to point…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(A\) speaks truth in \(75 \%\) of the cases and \(B\) in \(80 \%\) of the cases. Then, the probability that their statements about an incident do not match, isAP EAMCET 2016 Medium
- If \(f(x)=\left\{\begin{array}{cl}\frac{\sqrt{\pi}-\sqrt{\cos ^{-1} x}}{\sqrt{x+1}}, & x \neq-1 \\ \frac{1}{\sqrt{\lambda \pi}}, & x=-1\end{array}\right.\) is right
continuous at \(x=-1\), then \(\lambda=\)AP EAMCET 2023 Medium - If the variance of four numbers \(w, x, y\) and \(z\) is 9 , then the variance of \(5 w, 5 x, 5 y\) and \(5 z\) isAP EAMCET 2022 Easy
- \(\int \frac{x^2}{\left(x^2-1\right)\left(x^2+1\right)} d x=\)AP EAMCET 2023 Easy
- If a diagonal of a square is along the line \(8 x-15 y=0\) and one of its vertices is \((1,2)\), then the equations of the sides of the square passing through this vertex areAP EAMCET 2020 Easy
- If each of the observations \(x_1, x_2, \ldots, x_n\) is increased or decreased by \(k\), where \(k\) is a positive number, then the variance of the daAP EAMCET 2023 Easy
More PYQs from AP EAMCET
- A constant voltage of \(25 \mathrm{~V}\) is applied to a series \(L-R\) circuit at \(t=0\), by closing a switch. What is the potential difference across the resistor and the inductor at time \(t=0\) ?AP EAMCET 2011 Medium
- If is the perpendicular bisector of the line segment joining the points and , then the value of equals_____AP EAMCET 2021 Medium
- Identify the element which has highest second ionisation enthalpy.AP EAMCET 2022 Easy
- The coefficient of variation of \(9,3,11,5,7\), isAP EAMCET 2019 Easy
- If the straight line touches the curve at the point on it and thenAP EAMCET 2022 Hard
- What is the remainder of \(2 x^3-5 x^2+7\) when divided with \((x-2)\) ?AP EAMCET 2020 Easy