Question Detail

MTH 101 Analytical Geometry - The Circle Objective Question
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Question

What is the formula for the length of the tangent (TP) from an external point P(x₁, y₁) to the circle x² + y² + 2gx + 2fy + c = 0?
Options
A TP = √(x₁² + y₁² + 2gx₁ + 2fy₁ + c)
Correct Answer
B TP = √(x₁² + y₁² - 2gx₁ - 2fy₁ - c)
C TP = x₁² + y₁² + 2gx₁ + 2fy₁ + c
D TP = √(g² + f² - c)
Correct Answer

Option A is the correct answer.

Detailed Explanation

The length of the tangent from point P(x₁, y₁) to the circle is TP = √(x₁² + y₁² + 2gx₁ + 2fy₁ + c).

Hint

This is derived using the Pythagorean theorem in triangle CTP, where C is the centre.

Question Info

Course: MTH 101
Topic: Analytical Geometry - The Circle
Type: Objective
Difficulty: Not specified
Question 320 of 696
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