Question:
The locus of P such that the ratio of distance P from A(3, 1) and B(1, 2) is 5 : 4 is
The locus of P such that the ratio of distance P from A(3, 1) and B(1, 2) is 5 : 4 is
Updated On: Feb 24, 2026
- 81x2 - 92x + 81y2 - 180y = 35
- 81x2 + 92x + 81y2 - 19y = 35
- 81x2 - 48x + 81y2 + 20y = 35
- 81x2 - 90x + 81y2 - 180y = 35
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The Correct answer is option is (D) : 81x2 - 90x + 81y2 - 180y = 35
Was this answer helpful?
0
0
Top JEE Main Mathematics Questions
- For the matrices \( A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} \) and \( B = \begin{bmatrix} -29 & 49 \\ -13 & 18 \end{bmatrix} \), if \( (A^{15} + B) \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0\\ 0 \end{bmatrix} \), then among the following which one is true?}
Foot of perpendicular from origin on a line passing through $(1, 1, 1)$ having direction ratios $\langle 2, 3, 4 \rangle$, is:
- JEE Main - 2026
- Mathematics
- Geometry and Vectors
A line through $(1, 1, 1)$ and perpendicular to both $\hat{i} + 2\hat{j} + 2\hat{k}$ and $2\hat{i} + 2\hat{j} + \hat{k}$, let $(a, b, c)$ be foot of perpendicular from origin then $34 (a + b + c)$ is:
- JEE Main - 2026
- Mathematics
- Geometry and Vectors
- Sum of \( \frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \dots \) up to 8 terms is:
- JEE Main - 2026
- Mathematics
- Sequences and Series
- If $50 \left( \frac{2x}{1 + 3i} + \frac{y}{1 - 2i} \right) = 31 + 17i$ where $x, y \in R$ & $i = \sqrt{-1}$ then value of $10(x + 3y)$ is ________
- JEE Main - 2026
- Mathematics
- Complex Numbers and Quadratic Equations
View More Questions
Top JEE Main Coordinate Geometry Questions
- If eccentricity of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, which passes through the point $(3, 4)$ is $\frac{\sqrt{5}}{3}$, then length of latus rectum of ellipse, is :
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
A circle meets coordinate axes at 3 points and cuts equal intercepts. If it cuts a chord of length $\sqrt{14}$ unit on $x + y = 1$, then square of its radius is (centre lies in first quadrant):
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
- Let a circle of radius $4$ pass through the origin $O$, the points $A(-\sqrt{3}a,0)$ and $B(0,-\sqrt{2}b)$, where $a$ and $b$ are real parameters and $ab\neq0$. Then the locus of the centroid of $\triangle OAB$ is a circle of radius
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
- Let $A(1,0)$, $B(2,-1)$ and $C\left(\dfrac{7}{3},\dfrac{4}{3}\right)$ be three points. If the equation of the bisector of the angle $ABC$ is $\alpha x+\beta y=5$, then the value of $\alpha^2+\beta^2$ is
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
- A circle \(x^2+y^2=4\) intersects the \(x\)-axis at \(A(-2,0)\) and \(B(2,0)\). If two variable points \(P(2\cos\alpha,\,2\sin\alpha)\) and \(Q(2\cos\beta,\,2\sin\beta)\) vary on the circle such that \(\alpha-\beta=\dfrac{\pi}{2}\), then find the locus of the point of intersection of lines \(AP\) and \(BQ\).
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
View More Questions
Top JEE Main Questions
- For the matrices \( A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} \) and \( B = \begin{bmatrix} -29 & 49 \\ -13 & 18 \end{bmatrix} \), if \( (A^{15} + B) \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0\\ 0 \end{bmatrix} \), then among the following which one is true?}
- JEE Main - 2026
- Matrices
- A regular hexagon is formed by six wires each of resistance \( r \,\Omega \) and the corners are joined to the centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be
- JEE Main - 2026
- Nuclear physics
Object is placed at $40 \text{ cm}$ from spherical surface whose radius of curvature is $20 \text{ cm}$. Find height of image formed.
- In an equilateral prism the path of a ray is shown in the figure. Determine the refractive index of the prism.
- JEE Main - 2026
- Ray optics and optical instruments
- When $1$ g of compound $(X)$ is subjected to Kjeldahl's method for estimation of nitrogen, $15$ mL of $1$ M $\mathrm{H_2SO_4}$ was neutralized by ammonia evolved. The percentage of nitrogen in compound $(X)$ is:
- JEE Main - 2026
- Quantitative Analysis
View More Questions