If p and q are the lengths of the perpendiculars drawn from the origin on the linesयदि रेखाओं
If p and q are the lengths of the perpendiculars drawn from the origin on the lines
x sin θ + y cos θ = 2b sin θ cos θ
x cos θ − y sin θ = b cos 2θ
respectively, then the value of p² + q² is
यदि रेखाओं
x sin θ + y cos θ = 2b sin θ cos θ
x cos θ − y sin θ = b cos 2θ
पर मूलबिन्दु से डाले गए लम्बों की लम्बाइयाँ क्रमशः p और q हों, तो p² + q² का मान है
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Correct answer: (A) b²b²
Explanation
The distances from the origin are p = |2b sin θ cos θ| = b|sin 2θ| and q = b|cos 2θ|, so p² + q² = b²(sin²2θ + cos²2θ) = b².मूलबिन्दु से दूरियाँ p = |2b sin θ cos θ| = b|sin 2θ| और q = b|cos 2θ| हैं, अतः p² + q² = b²(sin²2θ + cos²2θ) = b²।