Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).
Solution and Explanation
Point (x, y) is equidistant from (3, 6) and (−3, 4).
\(\therefore\) \(\sqrt{(x-3)^2+(y-6)^2}=\sqrt{(x-(-3))^2+(y-4)^2}\)
\(\sqrt{(x-3)^2+(y-6)^2}=\sqrt{(x+3)^2+(y-4)^2}\)
\({(x-3)^2+(y-6)^2}={(x+3)^2+(y-4)^2}\)
\(36-16=6x+6x+12y-8y\)
\(20=12x+4y\)
\(3x+y=5\)
\(3x+y-5=0\)
Top Questions on Coordinate Geometry
- If the equation of the transverse common tangent of the circles \(x^2 + y^2 - 4x + 6y + 4 = 0\) and \(x^2 + y^2 + 2x - 2y - 2 = 0\) is \(ax + by + c = 0\), then \(\frac{a}{c} =\)
- TS EAMCET - 2024
- Mathematics
- Coordinate Geometry
- The equation of the pair of transverse common tangents drawn to the circles \( x^2 + y^2 + 2x + 2y + 1 = 0 \) and \( x^2 + y^2 - 2x - 2y + 1 = 0 \) is:
- TS EAMCET - 2024
- Mathematics
- Coordinate Geometry
Let \( F \) and \( F' \) be the foci of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) (where \( b<2 \)), and let \( B \) be one end of the minor axis. If the area of the triangle \( FBF' \) is \( \sqrt{3} \) sq. units, then the eccentricity of the ellipse is:
- AP EAPCET - 2024
- Mathematics
- Coordinate Geometry
A common tangent to the circle \( x^2 + y^2 = 9 \) and the parabola \( y^2 = 8x \) is
- AP EAPCET - 2024
- Mathematics
- Coordinate Geometry
If the equation of the circle passing through the points of intersection of the circles \[ x^2 - 2x + y^2 - 4y - 4 = 0, \quad x^2 + y^2 + 4y - 4 = 0 \] and the point \( (3,3) \) is given by \[ x^2 + y^2 + \alpha x + \beta y + \gamma = 0, \] then \( 3(\alpha + \beta + \gamma) \) is:
- AP EAPCET - 2024
- Mathematics
- Coordinate Geometry
Questions Asked in CBSE X exam
- Who was Henry? What role did he play in Ausable’s plan?
(The Midnight Visitor)- CBSE Class X - 2024
- The Midnight Visitor
- The roots of the quadratic equation \(x^2 + x – p (p + 1) = 0 \)are :
- CBSE Class X - 2024
- Quadratic Equations
- The pH of an aqueous solution of a salt is 9. The types of acid and base from which this salt is formed are:
- CBSE Class X - 2024
- Acids, Bases And Salts
- The sum of two numbers is 18, and the sum of their reciprocals is $\frac{1}{4}$. Find the numbers.
- CBSE Class X - 2024
- Linear Equations
- $ABCD$ is a trapezium with $AB \parallel DC$. $AC$ and $BD$ intersect at $E$. If $\triangle AED \sim \triangle BEC$, then prove that $AD = BC$.
- CBSE Class X - 2024
- Similarity of Triangles
Concepts Used:
Coordinate Geometry
The central idea in coordinate geometry is to assign numerical coordinates to points in a plane or space, which allows us to describe their positions and relationships using algebraic equations. The most common coordinate system is the Cartesian coordinate system, named after the French mathematician and philosopher René Descartes.