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What are the values of x y and k when the line y equals 3x plus 1 is a tangent to the circle x squared plus y squared equals k?
Wiki User
∙ 6y ago
If y = 3x + 1 is a tangent to x² + y² = k (k > 0 since it is a square), then where they meet has a repeated root; they meet at:
x² + (3x + 1)² = k
→ x² + 9x² + 6x + 1 - k = 0
→ 10x² + 6x + (1 - k) = 0
This is the point of contact when it has a repeated root which is when the discriminant is zero, ie when:
6² + 4 × 10 × (1 - k) = 0
→ 36 + 40 - 40k = 0
→ 40k = 4
→ k = 1/10
I guess for x & y you mean the point where y = 3x + 1 is a tangent to x² + y² = k, ie the point of contact.
The value of k can now be substituted into the equation of the point of contact:
10x² + 6x + (1 - k) = 0
→ 10x² + 6x + (1 - 1/10) = 0
→ 10x² + 6x + 9/10 = 0
→ x² + 6x/10 + 9/100 = 0
→ (x + 3/10)²
→ The point of contact is when x = -3/10
→ y = 3× -3/10 + 1 = 9/10 + 1 = 1/10
→ point of contact is (-3/10, 1/10) with k = 1/10
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∙ 6y ago
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What are the possible values of k when the line y equals kx -2 is a tangent to the circle y equals x2 -8x plus 7?
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What are the values of k when the line of y equals kx -2 is a tangent to the curve of y equals x squared -8x plus 7?
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What are the values of x and y when x minus y equals 0 and x squared plus y squared equals 18?
(x, y) = (-3, -3) or (3, 3)
What are the possible values of k in the line y equals kx -2 which is tangent to the curve y equals x squared -8x plus 7?
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