(5,2) বিন্দু থেকে $2x^2+2y^2-3x+7y+15=0$বৃত্তে অঙ্কিত স্পর্শকের দৈর্ঘ্য-

The answer is "6 একক" because it represents the length of the tangent drawn from the point (5,2) to the given circle described by the equation.

To understand how this is calculated:

    
1. First, we need the standard form of the circle's equation. The given equation is:
    
2. 2x² + 2y² - 3x + 7y + 15 = 0
    
3. We can rearrange and simplify it to find the center (h, k) and the radius (r) of the circle.
    
4. After finding these values, we can use the formula for the length of the tangent from a point (x₁, y₁) to a circle with center (h, k) and radius r:

The formula is:

Length of tangent = √((x₁ - h)² + (y₁ - k)² - r²)

Here, substituting (5, 2) and calculating the result leads to the tangent length being 6 একক. Thus, the option "d. 6 একক" is the correct answer.

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