Question:
Consider the points P(<span class="math-inline">(2, 1)</span>); Q(<span class="math-inline">(0, 0)</span>); R(<span class="math-inline">(4, -3)</span>) and the circle S : <span class="math-inline">x^2 + y^2 - 5x + 2y - 5 = 0</span>
exactly one point lies outside S
exactly two points lie outside S
all the three points lie outside S
none of the point lies outside S
Step-by-Step Solution
Key Concept: General
Let (h, k) be point of intersection of tangents then chord of contact is <br>yk = 4(x + h) <br>4x – yk + 4h = 0 <br>But given line is <br>x – y – 1 = 0 <br>Comparing (i) and (ii) <br>h = -1, k = 4 <br>point = (-1, 4)
Correct Answer: (-1, 4)