Question:
If two diameters of a circle are along the lines $2x-3y=5$ and $3x-4y=7$, then the centre is at
If two diameters of a circle are along the lines $2x-3y=5$ and $3x-4y=7$, then the centre is at
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Intersection of any two diameters always gives the coordinates of the center.
Updated On: Apr 28, 2026
- (1, 1)
- (-1, 1)
- (-1, -1)
- (1, -1)
- (1, -2)
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The Correct Option is D
Solution and Explanation
Step 1: Concept
The center of a circle is the point where its diameters intersect.
Step 2: Analysis
Solve the system: 1) $2x - 3y = 5 \times 3 \implies 6x - 9y = 15$ 2) $3x - 4y = 7 \times 2 \implies 6x - 8y = 14$
Step 3: Calculation
Subtracting (1) from (2): $y = -1$. Substitute $y = -1$ in $2x - 3(-1) = 5 \implies 2x + 3 = 5 \implies x = 1$. The centre is $(1, -1)$. Final Answer: (D)
The center of a circle is the point where its diameters intersect.
Step 2: Analysis
Solve the system: 1) $2x - 3y = 5 \times 3 \implies 6x - 9y = 15$ 2) $3x - 4y = 7 \times 2 \implies 6x - 8y = 14$
Step 3: Calculation
Subtracting (1) from (2): $y = -1$. Substitute $y = -1$ in $2x - 3(-1) = 5 \implies 2x + 3 = 5 \implies x = 1$. The centre is $(1, -1)$. Final Answer: (D)
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