In this question all units are in cm - OCR - GCSE Maths - Question 21 - 2019 - Paper 1

Given the coordinates of points A and B as follows:

• A = $(a, \sqrt{11})$
• B = $(b, \sqrt{11})$

Since both points have the same y-coordinate, we can calculate the length AB which is simply the distance between their x-coordinates:

$AB = |a - b|$

To find the values of a and b, we substitute the y-coordinate into the circle equation. Using the circle's equation:

$x^2 + y^2 = 36$

Substituting $y = \sqrt{11}$:

$x^2 + (\sqrt{11})^2 = 36$

This simplifies to:

$x^2 + 11 = 36$

Thus,

$x^2 = 36 - 11 = 25$

Therefore,

$x = \pm \sqrt{25} = \pm 5$

So, the coordinates are:

• A = (5, \sqrt{11})
• B = (-5, \sqrt{11})

Now, substituting into the length formula:

$AB = |5 - (-5)| = |5 + 5| = |10| = 10 \, cm$

Thus, the length AB is 10 cm.