Mathematics - Ellipse Question with Solution | TestHub

MathematicsEllipseGeneralHard3 minQB

MathematicsHardsingle choice

Passage / Comprehension

The ellipse $x^{2} / (lo g a)^{2} + y^{2} / (lo g b)^{2} = 1$ has eccentricity $1/ 2$ , and a related hyperbola is $x^{2} / (lo g_{b} a)^{2} - y^{2} = 1$ .

With the ellipse from above passage , tangents are drawn from $P = (1, 2)$ . If a contact point has eccentric angle $θ$ , which statement captures all possibilities?

Options:

Answer:

Solution:

The tangent condition is $cos θ /3 + sin θ = 1$ . One solution has $θ = π /2$ ; the other has $sec θ = 5/3, tan θ = 4/3$ , so no single $A - C$ describes all contacts.

Stream:JEESubject:MathematicsTopic:EllipseSubtopic:General

⏱ 3mℹ️ Source: QB

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