Question

if 3X + Y + K = 0 is a tangent to the circle, Xsquare + Y square is =10, then the value of k are​

Answer 1

Proper question :-

• If 3x + y + k = 0 is a tangent to the circle, x² + y² = 10 then the values of k are?

Solution :-

A equation of line is given to us :

• 3x + y + k = 0

So let us find out slope of it and y-intercept (C) :

• y = -3x - k

Therefore,

• m = -3 and C = -k

We're even provided with a equation of circle :

So using this equation we would be finding out the radius and center of circle.

General equation of circle is given by the formula,

• x² + y² + 2gx + 2fy + C = 0

So on comparing the general equation with the equation given (x² + y² - 10 = 0) we gets,

• g = 0 and f = 0

We know that,

• Centre of circle = (-g , -f)
• Radius of circle = √(g² + f² + c)

Using them we gets :

• Centre (C) = (0 , 0)
• Radius (r) = √[(0)² + (0)² - (-10)]
• Radius (r) = √(0 + 0 + 10)
• Radius (r) = √10

As we know that, condition of tangency where line will meet the circle :

• c = ± r √(m² + 1)

Substituting the values in it :

• c = ± √10 √[ (-3)² + 1]
• c = ± √10 √ (-3 × -3) + 1
• c = ± √10 √ (9 + 1)
• c = ± √10 . √10
• c = ± √100
• c = ± 10

Therefore , value of k is 10 and -10.

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