TS EAMCET · Maths · Straight Lines
The point \(P\) is equidistant from \(A(1,3)\), \(B(-3,5)\) and \(C(5,-1)\), then \(P A\) is equal to :
- A 5
- B \(5 \sqrt{5}\)
- C 25
- D \(5 \sqrt{10}\)
Answer & Solution
Correct Answer
(D) \(5 \sqrt{10}\)
Step-by-step Solution
Detailed explanation
Let co-ordinates of \(P\) are \((x, y)\). Since, \(P\) is equidistant from \(A, B, C\), then \(P A^2=P B^2\)...(i) and \(P B^2=P C^2\)...(ii) From Eq. (i), \((x-1)^2+(y-3)^2=(x+3)^2+(y-5)^2\) \(\Rightarrow \quad x^2+1-2 x+y^2+9-6 y\) \(=x^2+9+6 x+y^2+25-10 y\)…
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
- \(\begin{aligned} & A(\alpha, \beta)=\left[\begin{array}{ccc}\cos \alpha & \sin \alpha & 0 \\ -\sin \alpha & \cos \alpha & 0 \\ 0 & 0 & e^\beta\end{array}\right] \\ & \Rightarrow[A(\alpha, \beta)]^{-1}=\end{aligned}\)TS EAMCET 2011 Medium
- For all , if , thenTS EAMCET 2019 Easy
- \(\mathrm{t}_1, \mathrm{t}_2, \mathrm{t}_3, \ldots, \mathrm{t}_{\mathrm{n}}\) are positive integers, \(\mathrm{S}_{\mathrm{n}}=\mathrm{t}_1+\mathrm{t}_2+\mathrm{t}_3+\ldots+\mathrm{t}_{\mathrm{n}}, \mathrm{S}_1=1^2, \mathrm{~S}_2=3^2, \mathrm{~S}_3=6^2\), \(\mathrm{S}_4=10^2, \mathrm{~S}_5=15^2\) and similarly other terms are there. Following this pattern, if \(\mathrm{S}_{10}=\mathrm{k}^2\) then \(\mathrm{k}=\)TS EAMCET 2025 Medium
- The locus of the complex number \(z\) such that \(\arg \left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}\)TS EAMCET 2011 Hard
- \(A(-2,3)\) is a fixed point outside the parabola \(y^2=4 a x(a>0)\) and \(P\) is a point moving on the parabola. The locus of point \(Q\) which divides \(A P\) in the ratio \(3: 2\) is a conic. Then focus of that conic isTS EAMCET 2021 Hard
- If \(f:[0, \infty) \rightarrow[0, \infty)\) is defined by \(f(x)=\frac{x}{1+x}\), then \(f\) isTS EAMCET 2018 Easy
More PYQs from TS EAMCET
- \(\lim _{x \rightarrow \pi / 6}\left[\frac{3 \sin x-\sqrt{3} \cos x}{6 x-\pi}\right]\) is equal to :TS EAMCET 2003 Medium
- \(x\) grams of calcium carbonate was completely burnt in air. The weight of the solid residue formed is \(28 \mathrm{~g}\). What is the value of \(x\) (in grams)?TS EAMCET 2005 Easy
- If the angle between the asymptotes of a hyperbola is \(30^{\circ}\) then its eccentricity isTS EAMCET 2023 Medium
- Let \(n \in N\) which one of the following is true?TS EAMCET 2018 Easy
- Angles made with the \(X\)-axis by the two lines passing through the point \(P(1,2)\) and cutting the line \(x+y=4\) at a distance \(\frac{\sqrt{6}}{3}\) units from the point \(P\) areTS EAMCET 2020 Easy
- The ground state energy of hydrogen atom is -13.6 eV . The potential energy of the electron in the first excited state of hydrogen isTS EAMCET 2024 Easy