If x = h + aθ, y = k + bθ, then prove that : ((x-h)/(a) )² + ((y-k)/(b) )² = 1

((x-h)/(a) )² + ((y-k)/(b) )² = ²θ + ²θ = 1 (proved)

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 28(A)

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section C, question 28(A), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28(A) · 3 marks · Short answerIntroduction to Trigonometry

If $x = h + a cos θ$ , $y = k + b sin θ$ , then prove that : $(\frac{x - h}{a})^{2} + (\frac{y - k}{b})^{2} = 1$

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

Make cos θ the subject of the first equation and sin θ the subject of the second.

Hint 2

Square both results and add them.

Hint 3

Which identity links sin²θ and cos²θ?

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.

From $x = h + a cos θ$ : $x - h = a cos θ \Rightarrow \frac{x - h}{a} = cos θ$
1 mark
From $y = k + b sin θ$ : $y - k = b sin θ \Rightarrow \frac{y - k}{b} = sin θ$
1 mark
LHS $= (\frac{x - h}{a})^{2} + (\frac{y - k}{b})^{2} = cos^{2} θ + sin^{2} θ = 1 =$ RHS [since $sin^{2} θ + cos^{2} θ = 1$ ]
Hence proved.
1 mark

Answer: $(\frac{x - h}{a})^{2} + (\frac{y - k}{b})^{2} = cos^{2} θ + sin^{2} θ = 1$ (proved)

Where the marks are

Gets $\frac{x - h}{a} = cos θ$ (1 mark)
Gets $\frac{y - k}{b} = sin θ$ (1 mark)
Squares, adds and uses $sin^{2} θ + cos^{2} θ = 1$ to complete the proof (1 mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Proving Simple Trigonometric Identities

Practise this chapterBoard-style questions from Introduction to Trigonometry, 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 28(A)

Hints

Step-by-step solution

Revise the chapter

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