MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 23

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerCoordinate Geometry

The coordinates of the centre of a circle are $(x - 7, 2 x)$ . Find the value(s) of ' $x$ ', if the circle passes through the point $(- 9, 11)$ and has radius $52$ units.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/1/1.

Hints

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

Hint 1

The radius is the distance from the centre to any point on the circle.

Hint 2

Square both sides and simplify to a quadratic in x.

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.

Distance from the centre $(x - 7, 2 x)$ to $(- 9, 11)$ equals the radius: $(x - 7 + 9)^{2} + (2 x - 11)^{2} = 52$ .
½ mark
Squaring: $(x + 2)^{2} + (2 x - 11)^{2} = 50$ , so $x^{2} + 4 x + 4 + 4 x^{2} - 44 x + 121 = 50$ , which gives $5 x^{2} - 40 x + 75 = 0$ , i.e. $x^{2} - 8 x + 15 = 0$ .
½ mark
$(x - 3) (x - 5) = 0$ , so $x = 3$ or $x = 5$ .
1 mark

Answer: $x = 3$ or $x = 5$

Where the marks are

Sets up the distance formula equal to $52$ (½ mark)
Forms the quadratic $x^{2} - 8 x + 15 = 0$ (½ mark)
Gets x = 3 and x = 5 (½ + 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 paper2026 board paper, set 30/1/1 (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 2026: question 23

Hints

Step-by-step solution

Revise the chapter

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