AMU MCA 2016
The equation represents
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option D — a point circle
Detailed Solution
Complete the squares: .
So the equation is .
A sum of two squares is zero only when both are zero, so the only point is . This is a circle of radius zero, a point circle.
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.⚠ Common trap
The graph consists of one real point, not real lines, so options (A) and (B) are wrong. Note that the source key gave (A), which is incorrect.Quick tip
is a point circle when
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Ask a doubtMore Circle Questions
View all ›- Q1.Segments of the lines and are diameters of a circle of area 153.94 square units. Then the equation of this circle with integer radius is:
- Q2.Let AB be a chord of a circle subtending a right angle at the centre. Then, the locus of the centroid of the triangle PAB as P moves on the circle is
- Q3.The lines and are tangents to the same circle. The radius of this circle is
- Q4.Find the equation of the circle which passes through (-1, 1) and (2, 1), and has its centre on the line .
- Q5.If the circles and intersect orthogonally, then is
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- Q3.Let A be a real number. Then the roots of the equation are real and distinct if and only if Quadratic Equations
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Circle — Preparation
This question tests your understanding of Circle, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
In coordinate geometry, a circle is the set of points at a fixed distance (the radius) from a fixed point (the centre). This topic covers the standard equation (x - h)^2 + (y - k)^2 = r^2, the general equation x^2 + y^2 + 2gx + 2fy + c = 0 with centre (-g, -f), the diameter form, and parametric equations. Exam questions also test the position of a point relative to a circle, the condition for a line to be a tangent, equations of tangents and normals, the length of a tangent from an external point, and the intersection of two circles. The fastest approach is often to compare the distance from the centre to a line with the radius: equal means tangent, smaller means the line cuts the circle. Practise the circle questions below, each with a step-by-step solution.