![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
If the center of circle C is on the straight line 5x-3y = 8 and circle C is tangent to two coordinate axes, the equation of circle C is
Let the center of the circle be (x, y) tangent to the two coordinate axes, then | x | = R, | y | = RX = y = R or x = - y = R or - x = - y = R or - x = y = R. the center of the circle is on the straight line 5x-3y = 8 when x = y 5x-3x = 8, x = 4, y = 4, radius = | x | = 4 when x = - y 5x + 3x = 8, x = 1, y = - 1, radius = | x | = 1, so the equation of the circle is (x-1) & | 178; + (y + 1) & | 178; = 1
The standard equation for a circle whose center is on a straight line 5x-3y = 8 and tangent to two coordinate axes
If x = y, then x = y = 4; if x = - y, then x = 1, y = - 1, then the center of the circle is (4,4) or (1, - 1) because the radius is the distance from the center of the circle to the tangent line, that is, the center of the circle is (4,4)
The equation of a circle passing through point a (8,1) and tangent to two coordinate axes
Obviously, the circle passing through point (8,1) is located in the first quadrant. Let the equation of the circle be (x-a) & sup2; + (Y-A) & sup2; = A & sup2;, and a > 0 be substituted into point (8,1) to get (8-A) & sup2; + (1-A) & sup2; = A & sup2; that is, a & sup2; - 18a + 65 = 0, that is, (A-13) (a-5) = 0 to get a = 13 or a = 5. The circle is (X-13) & sup2; + (1-A) & sup2; = A & sup2
RELATED INFORMATIONS
- 1. The equation of a circle passing through point (8,1) and tangent to two coordinate axes
- 2. If f (x) = AX3 + 3x2 + 2 and f ′ (- 1) = 4, then the value of real number a is equal to______ ．
- 3. If the line ax + 2Y + 1 = 0 is perpendicular to the line x + 3y-2 = 0, what is the value of a?
- 4. If three straight lines x-2y + 1 = 0, x + 3y-1 = 0 and ax + 2y-3 = 0 have two different intersections, then a=______ ．
- 5. If the line ax + 2Y + 2 = 0 is parallel to the line 3x-y-2 = 0, find the distance between the two parallel lines
- 6. If the line ax-2y + 2 = 0 is parallel to the line x + (A-3) y + 1 = 0, then the real number J? Find the real number a?
- 7. Why is a = 2 a necessary and sufficient condition for "a line ax + 2Y = 0 parallel to a line x + y = 1"?
- 8. If the line ax + 2Y + 2 = 0 is parallel to the line 3x + ay + √ 6 = 0, what is the coefficient a
- 9. Given that line L1: ax-y + 2A = 0 and line L2: (2a-1) + ay + a = 0 are perpendicular to each other, find the value of A The solution should be detailed! Ha ha, thank you first
- 10. Let's know the line L1: y = - 1 / a times x + 2. L2: y = - ax + 1 + a (a is not equal to 0). If L1 is perpendicular to L2, find the value of A
- 11. "A = 3 or a = - 2" is the () condition that the line ax + 2Y + 3A = 0 and the line 3x + (A-1) y = A-7 are parallel and not coincident A. Sufficient and unnecessary B. necessary and not sufficient C. sufficient and necessary D. neither sufficient nor necessary
- 12. The curve C is a set of points whose product of the distances from two straight lines X + y = 0 and X-Y = 0 is 1. The trajectory equation of C is obtained
- 13. Solve the linear equation of point a (- 3,2) and the distance from the origin is 3
- 14. It is known that the eccentricity of ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is 1 / 2, the distance from the right focus to the straight line X / A + B / y = 1 d = √ 21 / 7, and O is the coordinate origin The equation of finding ellipse
- 15. It is known that the eccentricity e of the ellipse x 2A2 + y 2B2 = 1 (a > b > 0) is 63, and the distance between the straight line passing through points a (0, - b) and B (a, 0) and the origin is 32
- 16. The condition of X corresponding to the point on the number axis whose distance from the origin is less than 8 is? A - 8
- 17. The distance from point a (3, - 4) to the x-axis is -- the distance to the y-axis is -- the distance to the origin is-------
- 18. The distance from the origin to the line x-2y + 4 = 0 is
- 19. If the distance from the line L to the line x-2y + 4 = 0 is equal to the distance from the origin to the line L, then the equation of the line L is ﹣ U
- 20. The distance from the origin to the line x + 2y-5 = 0 is___ ．