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Mind Map: Conic Sections
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FAQs on Mind Map: Conic Sections
| 1. What's the difference between a circle, ellipse, parabola, and hyperbola in conic sections? |  |
Ans. Conic sections are curves formed by intersecting a plane with a double cone at different angles. A circle has a constant distance from one point; an ellipse has two focal points with constant sum of distances; a parabola has one focus and directrix with equal distance; a hyperbola has two foci with constant difference of distances. Each shape arises from varying the plane's angle relative to the cone's axis.
| 2. How do I find the equation of an ellipse when I'm given the foci and major axis length? | |
Ans. The standard ellipse equation is (x²/a²) + (y²/b²) = 1, where 'a' is the semi-major axis and 'b' is the semi-minor axis. Calculate 'c' (distance from centre to focus) using the given foci, then use c² = a² - b² to find b. Substitute these values into the standard form. This method applies whether the major axis is horizontal or vertical.
| 3. Why do parabola problems always mention the focus and directrix-what's their actual purpose? | |
Ans. The focus and directrix define a parabola's fundamental property: every point on the curve is equidistant from both. The focus (fixed point) and directrix (fixed line) determine the parabola's shape, width, and direction of opening. Using this distance property, students can derive the parabola equation and solve real-world trajectory or reflection problems in JEE Main and Advanced exams.
| 4. What are the eccentricity values for circles, ellipses, parabolas, and hyperbolas, and why do they matter? | |
Ans. Eccentricity (e) measures conic section shape: circle has e = 0; ellipse has 0 < e < 1; parabola has e = 1; hyperbola has e > 1. This parameter determines how "stretched" the curve is. In JEE exams, eccentricity helps classify conics quickly, predict curve behaviour, and solve problems involving tangent lines and normal equations without full calculations.
| 5. How do I find the equation of a tangent or normal line to a conic section at a given point? | |
Ans. For tangent lines, substitute the point's coordinates into the conic's equation using the tangent formula specific to each curve type. For ellipse: (xx₁/a²) + (yy₁/b²) = 1; for parabola: yy₁ = 2a(x + x₁); for hyperbola: (xx₁/a²) - (yy₁/b²) = 1. Normal lines are perpendicular to tangents, so find the tangent's slope first, then use slope = -1/m for the normal equation.
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Apr 20, 2026 Last updated
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