MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 29

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, section C, question 29, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 3 marks · Short answerCoordinate Geometry

Find a relation between $x$ and $y$ such that $P (x, y)$ is equidistant from the points A $(3, 5)$ and B $(7, 1)$ . Hence, write the coordinates of the points on x-axis and y-axis which are equidistant from points A and B.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Equate the squares of the distances PA and PB using the distance formula.

Hint 2

After expanding, the $x^{2}$ and $y^{2}$ terms cancel.

Hint 3

A point on the x-axis has y = 0; a point on the y-axis has x = 0.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

P is equidistant from A and B, so $P A = P B \Rightarrow P A^{2} = P B^{2}$ .
½ mark
$(x - 3)^{2} + (y - 5)^{2} = (x - 7)^{2} + (y - 1)^{2}$
$x^{2} - 6 x + 9 + y^{2} - 10 y + 25 = x^{2} - 14 x + 49 + y^{2} - 2 y + 1 \Rightarrow 8 x - 8 y = 16$
1 mark
$\Rightarrow x - y = 2$ is the required relation.
½ mark
On the x-axis $y = 0$ , so $x = 2$ : the point is $(2, 0)$ .
½ mark
On the y-axis $x = 0$ , so $y = - 2$ : the point is $(0, - 2)$ .
½ mark

Answer: $x - y = 2$ ; points (2, 0) and (0, −2)

Where the marks are

Uses $P A^{2} = P B^{2}$ (½ mark)
Applies the distance formula and expands correctly (1 mark)
Obtains $x - y = 2$ (½ mark)
Point on x-axis (2, 0) (½ mark)
Point on y-axis (0, −2) (½ mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Distance Formula

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/5/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2025: question 29

Hints

Step-by-step solution

Revise the chapter

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