Teachoo Quiz

10 Question MCQ (including Assertion)

Chapter 10 Class 11 Conic Sections | 10 questions | about 8 minutes

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Question 1 of 10
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Question 1 of 10
Assertion (A): A horizontal beam supported at ends \(12\) m apart deflects \(3\) cm at its center under a load. The deflection will be exactly \(1\) cm at a horizontal distance of \(2\sqrt{6}\) m from the center.
Reason (R): By placing the lowest point at the origin, the parabolic shape models as \(x^2 = 1200y\). A deflection of \(1\) cm translates to a height \(y = 0.02\) m from the vertex, solving for \(x = 2\sqrt{6}\).
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Question 2 of 10
Determine the equation of the hyperbola where foci are \((0, \pm 13)\) and the conjugate axis is of length \(24\).
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Question 3 of 10
A circle passes through the origin and makes intercepts \(a\) and \(b\) on the positive x-axis and y-axis respectively. What is the equation of this circle?
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Question 4 of 10
A water fountain sprays water in a parabolic path. It reaches a maximum height of \(4\) m at a horizontal distance of \(2\) m from its origin. What is the equation of the parabolic path?
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Question 5 of 10
Assertion (A): If \(a = b\) in the standard parametric equation of an ellipse, the resulting geometric curve behaves mathematically as a circle with an eccentricity of \(0\).
Reason (R): When \(a = b\), the focal distance \(c = \sqrt{a^2 - b^2}\) evaluates to \(0\), merging both foci directly with the center and effectively resulting in \(e = c/a = 0\).
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Question 6 of 10
A planet's orbit around its star is an ellipse with the star at one focus. If the maximum distance to the star is \(6 \times 10^8\) km and the minimum distance is \(4 \times 10^8\) km, what is the eccentricity of the orbit?
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Question 7 of 10
What is the maximum area of a rectangle that can be inscribed in the ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)?
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Question 8 of 10
Determine the equation of the circle with center \((0, 2)\) and radius \(2\).
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Question 9 of 10
Find the eccentricity of the hyperbola \(y^2 - 16x^2 = 16\).
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Question 10 of 10
Find the radius of the circle defined by the equation \(2x^2 + 2y^2 - x = 0\).
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