Question
Find a relation between $x$ and $y$ such that the point $(x, y)$ is equidistant from the points $(3, 6)$ and $(-3, 4).$
✓
Answer
Point $(x, y)$ is equidistant form $(3, 6)$ and $(-3, 4)$.
Therefore $\sqrt{(\text{x}-3)^2+(\text{y}-6)^2}=\sqrt{\big(\text{x}-(-3)\big)^2+{\text{(y}-4)^2}}$
$\sqrt{(\text{x}-3)^2+(\text{y}-6)^2}=\sqrt{(\text{x}+3)^2+(\text{y}-4)^2}$
Squaring both the side
$\big(\text{x}-3\big)^2+\big(\text{y}-6\big)^2=\big(\text{x}+3\big)^2+\big(\text{y}-4\big)^2$
$x^2 + 9 - 6x + y^2 + 36 - 12y = x^2 + 9 + 6x + y^2 + 16 - 8y$
$36 - 16 = 6x + 6x + 12y - 8y$
$20 = 12x + 4y$
$3x + y = 5$
Therefore $\sqrt{(\text{x}-3)^2+(\text{y}-6)^2}=\sqrt{\big(\text{x}-(-3)\big)^2+{\text{(y}-4)^2}}$
$\sqrt{(\text{x}-3)^2+(\text{y}-6)^2}=\sqrt{(\text{x}+3)^2+(\text{y}-4)^2}$
Squaring both the side
$\big(\text{x}-3\big)^2+\big(\text{y}-6\big)^2=\big(\text{x}+3\big)^2+\big(\text{y}-4\big)^2$
$x^2 + 9 - 6x + y^2 + 36 - 12y = x^2 + 9 + 6x + y^2 + 16 - 8y$
$36 - 16 = 6x + 6x + 12y - 8y$
$20 = 12x + 4y$
$3x + y = 5$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Prove The Theorem : If a line parallel to a side of a triangle intersects the remaining sides in two distinct points, then the line divides the sides in the same proportion.
Find the value of $k$, if $(5, k),(-3,1)$ and $(-7,-2)$ are collinear.
→Tickets numbered 1 to 30 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket drawn will be a multiple of 7 ?
In figure 3.94,
(1) m(arc CE) = 54°,
m(arc BD) = 23°, find measure of ∠CAE.
(2) If AB = 4.2, BC = 5.4,
AE = 12.0, find AD
(3) If AB = 3.6, AC = 9.0,
AD = 5.4, find AE
(1) m(arc CE) = 54°,
m(arc BD) = 23°, find measure of ∠CAE.
(2) If AB = 4.2, BC = 5.4,
AE = 12.0, find AD
(3) If AB = 3.6, AC = 9.0,
AD = 5.4, find AE
Short-Answer Questions:
Explain why 0.15015001500015... is an irrational number.
Explain why 0.15015001500015... is an irrational number.
A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets,
(1) a red balloon
(2) a blue balloon
(3) a green balloon.
(1) a red balloon
(2) a blue balloon
(3) a green balloon.
Solve the following systems of equations:
0.5x + 07y = 0.74
0.3x + 0.5y = 0.5
Prove : $\frac{\sin \theta+\tan \theta}{\cos \theta}=\tan \theta(1+\sec \theta)$
→ABC is a triangle in which $\angle\text{A}=90^\circ,\ \text{AN}\perp\text{BC}$ BC = 12cm and AC = 5cm. Find the ratio of the area of $\triangle\text{ANC}$ and $\triangle\text{ABC}.$
→Check whether 301 is in the sequence
$5,11,17,23, \ldots \text { ? }$
→$5,11,17,23, \ldots \text { ? }$