✓ Board-verified↻ asked 2×
Mathematics · 2026 · 2 marks
CBSE 2026 · Region 1 · Set 1 · Q23
The coordinates of the centre of a circle are ( $\displaystyle x-7,2 x$ ). Find the value(s) of ' $\displaystyle x$ ', if the circle passes through the point ( $\displaystyle -9,11$ ) and has radius $\displaystyle 5 \sqrt{2}$ units.
Marking-scheme solution
\[\begin{aligned}
& \sqrt{(x-7+9)^{2}+(2 x-11)^{2}}=5 \sqrt{2} \\
& \Rightarrow(x+2)^{2}+(2 x-11)^{2}=50 \\
& \Rightarrow 5 x^{2}-40 x+75=0 \text { or } x^{2}-8 x+15=0 \\
& \Rightarrow(x-5)(x-3)=0 \\
& \therefore x=3,5
\end{aligned}
\]
More from Coordinate Geometry
- The line segment joining the points P(-4,-2) and Q(10,4) is divided by y-axis in the ratio2026 · asked 3×
- Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also…2025 · asked 3×
- If Q(0,1) is equidistant from P(5,-3) and R(x, 6), find the values of x.2023 · asked 3×
- The coordinates of the end points of the line segment AB are A(-2, -2) and B(2,-4). P is the point on AB such…2025 · asked 3×
- Find a relation between x and y such that P(x, y) is equidistant from the points A(3, 5) and B(7, 1). Hence,…2025 · asked 3×
- If the diagonals of a quadrilateral divide each other proportionally, then it is a:2024 · asked 3×
- Two of the vertices of Δ PQR are P(-1,5) and Q(5,2). The coordinates of a point which divides PQ in the ratio…2025 · asked 3×
- A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden…2024 · asked 3×
CBSE Class 10 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.