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Points A(–1, y) and B(5, 7)… (Class 10 Maths 2024, Q23b)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 23(b)

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section B, question 23(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(b) · 2 marks · Very short answerCoordinate Geometry

Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y) such that AB is a diameter of the circle. Find the value of . Also, find the radius of the circle.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

Where does the centre of a circle lie on any of its diameters?

Hint 2

Use the mid-point formula for the y-coordinate and set it equal to –3y. Then find OB with the distance formula.

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.

  1. AB is a diameter, so the centre O is the mid-point of AB. Equate the y-coordinate of the mid-point of A(–1, y) and B(5, 7) with that of O(2, –3y): . (The x-coordinate checks: .)

    ½ mark

  2. . So A is and O is .

    ½ mark

  3. Radius units.

    1 mark

Answer: y = –1; radius = 5 units

Where the marks are

  • Uses that the centre is the mid-point of diameter AB and writes (½ mark)
  • Gets (½ mark)
  • Uses the distance formula to get radius = 5 units (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/3/1 (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.