TS EAMCET · Maths · Straight Lines
If a line L passing through the point \(\mathrm{A}(-2,4)\) makes an angle of \(60^{\circ}\) with the positive direction of X -axis in anti-clockwise direction and \(\mathrm{B}(p, q)\) lying in the \(3^{\text {rd }}\) quadrant is a point on L at the distance of 6 units from the point A, then \(\sqrt{p^2+q^2-8 q}=\)
- A 6
- B 7
- C 8
- D 9
Answer & Solution
Correct Answer
(A) 6
Step-by-step Solution
Detailed explanation
\(p = -2 - 6 \cos 60^{\circ} = -2 - 6(1/2) = -5\) \(q = 4 - 6 \sin 60^{\circ} = 4 - 6(\sqrt{3}/2) = 4 - 3\sqrt{3}\) \(\sqrt{p^2 + q^2 - 8q} = \sqrt{p^2 + (q-4)^2 - 16}\) \(= \sqrt{(-5)^2 + (4 - 3\sqrt{3} - 4)^2 - 16}\) \(= \sqrt{25 + (-3\sqrt{3})^2 - 16}\)…
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 \(A=\left[\begin{array}{ll}0 & 3 \\ 0 & 0\end{array}\right]\) and \(f(x)=x+x^2+x^3+\ldots . .+x^{2023}\) then \(\mathrm{f}(\mathrm{A})+\mathrm{I}=\)TS EAMCET 2023 Easy
- The point \(P(1,4)\) occupies the positions \(A, B\) and \(C\) respectively after undergoing the following three transformation successively. I. Reflection about the line \(y=x\). II. Translation through a distance of 1 unit along the positive direction of \(X\)-axis. III. Rotation of the line \(O B\) through an angle \(\frac{\pi}{4}\) about the origin in the anti-clockwise direction. Then, the coordinates of \(C\) areTS EAMCET 2019 Easy
- If the functions \(f\) and \(g\) are defined by \(f(x)=3 x-4, \quad g(x)=2+3 x \quad\) for \(\quad x \in R\) respective, then \(g^{-1}\left(f^{-1}(5)\right)\) is equal toTS EAMCET 2002 Hard
- Given that the roots of \(x^3+3 p x^2+3 q x+r=0\) are in harmonic progression. Then,TS EAMCET 2018 Easy
- If \(P\left(\frac{\pi}{4}\right), Q\left(\frac{\pi}{3}\right)\) are two points on the circle \(x^2+y^2-2 x-2 y-1=0\), then the slope of the tangent to this circle which is parallel to the chord \(P Q\) isTS EAMCET 2024 Medium
- The length of the segment of the tangent line to the curve \(x=a \cos ^3 t, y=\alpha \sin ^3 t\), at any point on the curve cut off by the coordinate axes isTS EAMCET 2016 Hard
More PYQs from TS EAMCET
- If \(C\) the velocity of light, \(h\) Planck's constant and \(G\) gravitational constant are taken as fundamental quantities, then the dimensional formula of mass isTS EAMCET 2014 Easy
- A random variable takes the values and such that . If is the variance and is the mean of , thenTS EAMCET 2018 Hard
- Which one of the following reactions does not occur?TS EAMCET 2008 Medium
- If denotes the greatest integer function of and , thenTS EAMCET 2022 Easy
- A random variable \(\mathrm{X}\) has the following probability distribution \begin{array}{|l|c|c|c|c|c|c|c|c|c|} \hline \mathbf{X}=\mathbf{x}_{\mathrm{i}}: & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \ \hline \mathbf{P}\left(\mathbf{X}=\mathbf{x}_{\mathrm{i}}\right): & 10 \mathrm{k} & 9 \mathrm{k} & 8 \mathrm{k} & 8 \mathrm{k} & 6 \mathrm{k} & 5 \mathrm{k} & 4 \mathrm{k} & 3 \mathrm{k} & \mathrm{k} \ \hline \end{array} where \(\mathrm{k}\) is a real number If \(\mathrm{A}=\left\{x_i / x_i\right.\) is a prime number \(\}\) and \(\mathrm{B}=\left\{x_i / x_i>5\right\}\) are two events, then \(P(A \cup B)=\)TS EAMCET 2022 Medium
- If the area of a circle increases at the rate of \(\frac{1}{\sqrt{\pi}}\) sq. units/sec, then the rate (in units/sec) at which the perimeter of the circle changes, when perimeter is \(\sqrt{\pi}\) units, isTS EAMCET 2020 Easy