JEE Main Mathematics: Analytical Geometry Practice Questions
9 free multiple-choice questions on Analytical Geometry for JEE Main Mathematics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.
Practice thousands more Analytical Geometry questions in the app →Q1. If a chord of a circle is tangent to a semicircle at its midpoint, what is the relationship between the chord and the diameter?
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Correct answer: C — The chord is perpendicular to the diameter.
If a chord is tangent to the semicircle at its midpoint, the tangent line (the chord) must be perpendicular to the radius (which is part of the diameter) at that point. Therefore, the chord is perpendicular to the diameter.
Q2. The locus of a point that moves such that the sum of its distances from two fixed points (foci) is constant is a:
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Correct answer: B — Ellipse
The definition of an ellipse is the set of all points such that the sum of the distances from two fixed points (foci) is constant.
Q3. A circle has its center at C(0, 0) and a radius of r=3. Determine the number of points where the circle intersects the line 3x + 4y = 10.
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Correct answer: B — 2
The distance d from the center (0, 0) to the line 3x + 4y - 10 = 0 is d = (|3(0) + 4(0) - 10|)/(√(3² + 4²)) = 10/5 = 2. Since the distance d=2 is less than the radius r=3, the line intersects the circle at two distinct points.
Q4. Two lines L₁ and L₂ intersect at point P. If a third line L₃ also passes through P, what property does L₃ have with respect to L₁ and L₂ at point P?
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Correct answer: C — It forms an angle θ with both L₁ and L₂.
If three distinct lines (L₁, L₂, L₃) intersect at a single point P, the lines form various angles. While L₃ is not necessarily the angle bisector, it simply forms angles with L₁ and L₂ at P. The most general statement is that L₃ passes through the intersection point P.
Q5. Find the locus of the point P(x, y) which moves such that its coordinates satisfy the equation 2x + 3y = 10.
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Correct answer: C — 2x + 3y = 10
If the locus of a point is defined by a linear equation, then the coordinates (x, y) of the point must satisfy that equation.
Q6. What is the relationship between the semi-major axis (a) and the semi-minor axis (b) in the standard form equation of an ellipse?
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Correct answer: A — a² = b² - c²
In an ellipse, the relationship between the semi-major axis (a), semi-minor axis (b), and the distance from the center to the focus (c) is a² = b² + c².
Q7. For a hyperbola, the eccentricity (e) is always greater than which value?
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Correct answer: C — 1
For a hyperbola, the eccentricity (e) must be greater than 1 (e>1).
Q8. If a line intersects a circle at exactly one point, what geometric relationship between the line and the circle is established?
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Correct answer: C — The line is tangent to the circle
When a straight line intersects a circle at exactly one point, it means the line touches the circle at that single point, establishing that the line is tangent to the circle.
Q9. In the parametric representation of a conic section, the parameter θ is typically related to the angle of the line segment connecting the point to the focus or directrix. This is characteristic of which type of parametric representation?
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Correct answer: D — Parametric form using θ
The use of a parameter like θ in conjunction with trigonometric functions (like cos θ, sin θ) is the standard way to represent conic sections parametrically, linking the coordinates to an angular parameter.
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