Select Goal &
City
Select Goal
Explore
Question:
If P(6, 1) be the orthocentre of the triangle whose vertices are A(5, –2), B(8, 3) and C(h, k), then the point C lies on the circle.
If P(6, 1) be the orthocentre of the triangle whose vertices are A(5, –2), B(8, 3) and C(h, k), then the point C lies on the circle.
Updated On: Nov 26, 2024
- $x^2 + y^2 - 65 = 0$
- $x^2 + y^2 - 74 = 0$
- $x^2 + y^2 - 61 = 0$
- $x^2 + y^2 - 52 = 0$
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
To find the coordinates of \( C \), we proceed with the slopes of sides and the equations of lines.
1. Slope of \( AD \):
\[ \text{Slope of } AD = 3 \]
2. Slope of \( BC \):
\[ \text{Slope of } BC = -\frac{1}{3} \]
Equation of \( BC \):
\[ 3y + x - 17 = 0 \]
3. Slope of \( BE \):
\[ \text{Slope of } BE = 1 \]
4. Slope of \( AC \):
\[ \text{Slope of } AC = -1 \]
Equation of \( AC \):
\[ x + y - 3 = 0 \]
Solving these equations, we find:
\[ \text{Point } C \text{ is } (-4, 7) \]
Since \( C \) lies on the circle, we have:
\[ x^2 + y^2 - 65 = 0 \]
Was this answer helpful?
0
0
Top Questions on Triangles
- Let ABC be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle ABC and the same process is repeated infinitely many times. If P is the sum of perimeters and Q is be the sum of areas of all the triangles formed in this process, then:
- In a triangle $ABC$, $BC = 7$, $AC = 8$, $AB = \alpha \in \mathbb{N}$ and $\cos A = \frac{2}{3}$. If \[ 49 \cos(3C) + 42 = \frac{m}{n}, \] where $\gcd(m, n) = 1$, then $m + n$ is equal to ________.
- Let $P(\alpha, \beta, \gamma)$ be the image of the point $Q(3, -3, 1)$ in the line \[\frac{x - 0}{1} = \frac{y - 3}{1} = \frac{z - 1}{-1}\]and $R$ be the point $(2, 5, -1)$. If the area of the triangle $PQR$ is $\lambda$ and $\lambda^2 = 14K$, then $K$ is equal to:
- Consider a triangle \( \triangle ABC \) having the vertices \( A(1, 2) \), \( B(\alpha, \beta) \), and \( C(\gamma, \delta) \) and angles \( \angle ABC = \frac{\pi}{6} \) and \( \angle BAC = \frac{2\pi}{3} \). If the points \( B \) and \( C \) lie on the line \( y = x + 4 \), then \( \alpha^2 + \gamma^2 \) is equal to \( \dots \).
- If the orthocentre of the triangle formed by the lines 2x + 3y – 1 = 0, x + 2y – 1 = 0 and ax + by – 1 = 0, is the centroid of another triangle, whose circumecentre and orthocentre respectively are (3, 4) and (–6, –8), then the value of |a– b| is_____.
View More Questions
Questions Asked in JEE Main exam
The value \( 9 \int_{0}^{9} \left\lfloor \frac{10x}{x+1} \right\rfloor \, dx \), where \( \left\lfloor t \right\rfloor \) denotes the greatest integer less than or equal to \( t \), is ________.
- JEE Main - 2024
- Definite Integral
- Among \(\text{CrO}\), \(\text{Cr}_2\text{O}_3\), and \(\text{CrO}_3\), the sum of spin-only magnetic moment values of basic and amphoteric oxides is ______ \( \times 10^{-2} \, \text{BM} \) (nearest integer).
Given: Atomic number of Cr is 24. - The major products from the following reaction sequence are product A and product B.
- JEE Main - 2024
- Aromaticity & chemistry of aromatic compounds
- An ideal gas, \(\overline{C_V} = \frac{5}{2} R\), is expanded adiabatically against a constant pressure of 1 atm until it doubles in volume.
If the initial temperature and pressure are \(298 \, \text{K}\) and \(5 \, \text{atm}\), respectively, then the final temperature is ______ \( \, \text{K} \) (nearest integer).
Given: \(\overline{C_V}\) is the molar heat capacity at constant volume.- JEE Main - 2024
- Adiabatic Processes
- Frequency of the de-Broglie wave of the electron in Bohr's first orbit of the hydrogen atom is ______ \( \times 10^{13} \, \text{Hz} \) (nearest integer).
Given:\(R_H\) (Rydberg constant) = \(2.18 \times 10^{-18} \, \text{J}\)\(h\) \((\)Planck's constant)= \(6.6 \times 10^{-34}\)\(\text{J.s}\)- JEE Main - 2024
- Atomic Structure
View More Questions
SUBSCRIBE TO OUR NEWS LETTER
COLLEGE NOTIFICATIONSEXAM NOTIFICATIONSNEWS UPDATES
Download the Collegedunia app on 
© 2024 Collegedunia Web Pvt. Ltd. All Rights Reserved