Question

The number of real tangents that can be drawn to the ellipse $3x²+5y²=32$ passing through (3, 5) is

• A. 0
• B. 1
• C. 2
• D. infinite

Hint:

The number of real tangents that can be drawn to the ellipse $3x=32$ passing through (3, 5) is

Answer 1

The Correct Option is C

Step 1: Concept
The number of real tangents depends on whether the point is outside, on, or inside the ellipse.
Step 2: Analysis
Substitute (3, 5) into $S = 3x^2 + 5y^2 - 32$.
Step 3: Evaluation
$S_1 = 3(3)^2 + 5(5)^2 - 32 = 27 + 125 - 32 = 120$. Since $S_1>0$, the point lies outside the ellipse.
Step 4: Conclusion
From any point outside an ellipse, exactly two real tangents can be drawn.
Final Answer: (c)