Question Detail

MTH 101 Analytical Geometry - The Circle Objective Question
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Question

What is the formula for the equation of a tangent to the general circle x² + y² + 2gx + 2fy + c = 0 at the point (x₁, y₁)?
Options
A xx₁ + yy₁ + g(x - x₁) + f(y - y₁) + c = 0
B xx₁ + yy₁ + g(x + x₁) + f(y + y₁) + c = 0
Correct Answer
C xx₁ + yy₁ + gx + fy + c = 0
D x + x₁ + y + y₁ + 2g + 2f + c = 0
Correct Answer

Option B is the correct answer.

Detailed Explanation

For the general circle x² + y² + 2gx + 2fy + c = 0, the equation of the tangent at (x₁, y₁) is xx₁ + yy₁ + g(x + x₁) + f(y + y₁) + c = 0.

Hint

This is a standard transformation of the general circle equation.

Question Info

Course: MTH 101
Topic: Analytical Geometry - The Circle
Type: Objective
Difficulty: Not specified
Question 316 of 696
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