MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 23

Set in the CBSE Class 10 board exam of 2025, 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 $(2 a, a - 7)$ . Find the value(s) of 'a' if the circle passes through the point $(11, - 9)$ and has diameter $102$ units.

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

Hints

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

Hint 1

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

Hint 2

Square both sides of the distance formula with radius $52$ and simplify to a quadratic in $a$ .

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.

Diameter $= 102$ , so radius $= 52$ units and radius $^{2} = 50$ .
½ mark
The distance from the centre $(2 a, a - 7)$ to the point $(11, - 9)$ equals the radius. By the distance formula:
$(2 a - 11)^{2} + (a - 7 + 9)^{2} = 50$ , i.e. $(2 a - 11)^{2} + (a + 2)^{2} = 50$
½ mark
$4 a^{2} - 44 a + 121 + a^{2} + 4 a + 4 = 50 \Rightarrow 5 a^{2} - 40 a + 75 = 0 \Rightarrow a^{2} - 8 a + 15 = 0$
½ mark
$(a - 5) (a - 3) = 0 \Rightarrow a = 5$ or $a = 3$
½ mark

Answer: a = 5 or a = 3

Where the marks are

Finds radius $52$ units (½ mark)
Applies the distance formula equated to the radius (½ mark)
Obtains $a^{2} - 8 a + 15 = 0$ (½ mark)
Gets $a = 5, 3$ (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 30/1/1 (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 2025: question 23

Hints

Step-by-step solution

Revise the chapter

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