Delhi University MCA Geometry Previous Year Questions (PYQs)
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Showing 10 questions
The locus of the point (α, β) such that the line y = αx + β, become a tangent to the hyperbola 9x2 - 4x2 = 36, is
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Solution
The area (in squares units) of the quadrilateral
formed by the tangent lines drawn to the ellipse 
at the ends of its two latus rectums is
at the ends of its two latus rectums is1
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Solution
The equation of common tangent to the curve y2 = 8x and xy = - 1 is
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Solution
Solution:
Let the common tangent be: $$y = mx + c$$ For curve \( y^2 = 8x \):Condition for tangency gives: $$mc = 2 \quad \text{(1)}$$ For curve \( xy = -1 \):
Condition for tangency gives: $$c^2 = 4m \quad \text{(2)}$$ Substitute \( c = \frac{2}{m} \) from (1) into (2): $$\left(\frac{2}{m}\right)^2 = 4m \Rightarrow \frac{4}{m^2} = 4m \Rightarrow m^3 = 1 \Rightarrow m = 1$$ Then, \( c = \frac{2}{1} = 2 \)
Final Answer:
$$\boxed{y = x + 2}$$
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