The distance between the points (aθ + bθ, 0) and (0, aθ - bθ) is (A) √(a² + b²) (B) a² - b² (C) √(a² - b²) (D) a² + b²

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 15

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section A, question 15, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q15 · 1 mark · MCQCoordinate Geometry

The distance between the points $(a cos θ + b sin θ, 0)$ and $(0, a sin θ - b cos θ)$ is

(A) $a^{2} + b^{2}$
(B) $a^{2} - b^{2}$
(C) $a^{2} - b^{2}$
(D) $a^{2} + b^{2}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

Apply the distance formula.

Hint 2

The $2 ab sin θ cos θ$ terms cancel.

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.

$d^{2} = (a cos θ + b sin θ)^{2} + (a sin θ - b cos θ)^{2} = a^{2} (cos^{2} θ + sin^{2} θ) + b^{2} (sin^{2} θ + cos^{2} θ) = a^{2} + b^{2}$ (cross terms cancel).
$d = a^{2} + b^{2}$ .
1 mark

Answer: $a^{2} + b^{2}$ , option (A)

Where the marks are

Distance formula with cancellation gives $a^{2} + b^{2}$ (1 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 30/4/1 (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 15

Hints

Step-by-step solution

Revise the chapter

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