Circles
General
Grade 11

Question:

Tangents are drawn to a unit circle with centre at the origin from each point on the line <span class="math-inline">2x + y = 4</span>. Then the equation to the locus of the middle point of the chord of contact is -
2(x^2 + y^2) = x + y
2(x^2 + y^2) = x + 2y
4(x^2 + y^2) = 2x + y
none

Step-by-Step Solution

Key Concept: General
Given parabolas y²=4ax and y²=4c(x-b) have common normals. Then equation of normals in terms of slopes are y = mx - 2am - am³ and y = m(x - b) - 2cm - cm³ respectively then normals must be identical, compare the co-efficients.
Correct Answer: b/a - c > 2

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