AP EAMCET · Maths · Circle
The angle between the tangents drawn from a point \((4,3)\) to the circle \(x^2+y^2-2 x-4 y=0\) is
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
Center \(C=(1,2)\), radius \(r=\sqrt{1^2+2^2-0}=\sqrt{5}\). Distance \(d=\sqrt{(4-1)^2+(3-2)^2}=\sqrt{3^2+1^2}=\sqrt{10}\). \(\sin\theta = \frac{r}{d} = \frac{\sqrt{5}}{\sqrt{10}} = \frac{1}{\sqrt{2}}\). \(\theta = \frac{\pi}{4}\). Angle between tangents…
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
- If \(A\) and \(B\) are positive acute angles satisfying \(3 \cos ^2 A+2 \cos ^2 B=4\) and \(\frac{3 \sin A}{\sin B}=\frac{2 \cos B}{\cos A}\), then \(A+2 B=\)AP EAMCET 2025 Medium
- For \(x \in I R, 3 \cos (4 x-5)+4\) lies in the intervalAP EAMCET 2004 Easy
- The equation of the ellipse having a vertex at \((6,1)\), a focus at \((4,1)\) and the eccentricity \(\frac{3}{5}\) isAP EAMCET 2018 Easy
- 7 relatives of a man comprise 4 ladies and 3
gentlemen. His wife also has 7 relatives − 3 of
them are ladies and 4 are gentlemen. In how
many ways can they invite a dinner party of
3 ladies and 3 gentlemen, so that there are
3 of man’s relative and 3 of wife’s relative?AP EAMCET 2021 Medium - A random variable X follows a binomial distribution in which the difference between its mean and variance is 1. If \(2 \mathrm{P}(\mathrm{x}=2)=3 \mathrm{P}(\mathrm{x}=1)\), then \(\mathrm{n}^2 \mathrm{P}(\mathrm{x}>1)=\)AP EAMCET 2025 Medium
- If the vectors \(\vec{a}=2 \hat{i}-\hat{j}+\hat{k}, \vec{b}=\hat{i}+2 \hat{j}-3 \hat{k}\), \(\vec{c}=3 \hat{i}+p \hat{j}+5 \hat{k}\) are coplanar then \(p=\)AP EAMCET 2024 Easy
More PYQs from AP EAMCET
- In which one of the following pairs, both oxides are acidic?AP EAMCET 2023 Easy
- Compound \(X\) is anhydride of sulphuric acid. The number of \(\sigma\)-bonds and the number of \(\pi\)-bonds present in \(X\) are, respectively :AP EAMCET 2003 Easy
- If the \(y\)-intercept of the perpendicular bisector of the line segment joining \(\mathrm{P}(1,4)\) and \(\mathrm{Q}(\mathrm{k}, 3)\) is -4 , then a possible value of \(k\) isAP EAMCET 2023 Medium
- A gas of mass ' \(\mathrm{m}\) ' and molecular weight ' \(\mathrm{M}\) ' is flowing in an insulated tube with a velocity ' \(2 \mathrm{~V}\) '. If the flow of the gas is suddenly stopped and all the kinetic energy is utilized to compress the gas, the increases in the temperature of the gas is ( \(\gamma\) is ratio of specific heats, \(\mathrm{R}\) is universal gas constant)AP EAMCET 2023 Hard
- In \(\triangle \mathrm{ABC}\), if a \(\cos ^2 \frac{\mathrm{C}}{2}+\cos ^2 \frac{\mathrm{A}}{2}=\frac{3 \mathrm{~b}}{2}\), then \(\mathrm{a}+\mathrm{c}: \mathrm{b}=\)AP EAMCET 2023 Hard
- \(\int_0^{\pi / 4}\left(\tan ^2 x-\tan ^4 x\right) d x=\)AP EAMCET 2020 Hard