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Given that the center of the circle is on the straight line 3x + 4y-5 = 0 and tangent to both coordinate axes, the equation of the circle is obtained,
Let the center of the circle be (a, (5-3a) / 4) and tangent to the coordinate axis
The radius is equal to the absolute value of the coordinates
That is: r = | a | = | 5-3a | / 4
a=(5-3a)/4--> a=5/7
-a=(5-3a)/4-->a=-5
So there are two circles, and the equation is:
(x-5/7)^2+(y-5/7)^2=25/49
(x+5)^2+(y-5)^2=25
The equation for finding a circle whose center is on the straight line 3x-4y = 7 and tangent to both coordinate axes
It's better to write by hand
Let the center of the circle be (a, b), the radius be r, and the circle is tangent to the two coordinate axes. It shows that: a = ± B (1) a = B, so 3a-4a = 7 is solved, a = b = - 7. Then, the standard equation of r = 7 circle is: (X-7) square + (Y-7) square = 49 (2) a = - B, so 3A + 4A = 7 is solved, a = 1, B = - 1. Then, the standard equation of R = 1 circle is
Circle tangent to both axes and line 3x + 4y-4 = 0
1, the equation of the circle in the first quadrant which is tangent to the two coordinate axes and the line 3x + 4y-4 = 0____________
If the secant of circle x ^ 2 + y ^ 2-8x-2y + 12 = 0 is made through point P (3,0), then the linear equations of the longest and shortest chord are_____________
3. Given that P is a point on the circle (X-2) ^ 2 + (Y-5) ^ 2 = 1 and Q (2,3), then the maximum inclination angle of the line PQ___________ , minimum_________
4. Find a point P on the straight line X-Y + 2 √ 2 = 0, so that the tangent length from P to the circle x ^ 2 + y ^ 2 = 1 is the shortest, then the coordinate of point P is_________
1, the equation of the circle in the first quadrant which is tangent to the two coordinate axes and the line 3x + 4y-4 = 0____________ The distance between 3x + 4y-4 = 0 and the intersection a (4 / 3,0) of x-axis, and the intersection B (0,1) of y-axis is ab = ((16 / 9) + 1) ^ (1 / 2) = 5 / 3. Suppose the radius of circle R, then the area of triangle ABO = (1 / 2) * (4 / 3) * 1 = (1 / 2)
RELATED INFORMATIONS
- 1. The equation of the circle with the diameter of the line segment between the two coordinate axes 3x-4y + 12 = 0 is______ ．
- 2. The equation of circle C is () A. (x−12)2+(y−3)2＝52B. (x−12)2+(y+3)2＝52C. (x+12)2+(y−3)2＝254D. (x+12)2+(y+3)2＝254
- 3. It is known that the center coordinate of circle C is (- 1,3), and the circle and the straight line x + Y-3 = 0 intersect at P and Q, and OP is perpendicular to OQ, O is the origin of coordinates, so the equation of circle C is obtained
- 4. The center of the circle is at the origin, and the radius is 3 It's a process,
- 5. The equation of the circle with (3,4) as the center and passing through the origin is
- 6. The equation of the circle with three points P (0,2 times root sign 3) m (1, root sign 7) n (- 2,4) is solved and transformed into standard form
- 7. If the center of the circle is on the x-axis and passes through the point (3, root 3) (0,0), find the equation of similar circle
- 8. Given that the center of the circle is on the x-axis, the radius is 5 and the chord length with a (5,4) as the midpoint is 25, then the equation of the circle is () A. (x-3) 2 + y2 = 25B. (X-7) 2 + y2 = 25C. (x ± 3) 2 + y2 = 25d. (x-3) 2 + y2 = 25 or (X-7) 2 + y2 = 25
- 9. What does (x + 2) & sup2; + Y & sup2; = 5 say about the equation of a circle symmetrical at the origin
- 10. The positional relationship of circle C1: x2 + y2 = 4 and C2: x2 + y2-6x + 8y-24 = 0 is______ ．
- 11. Given the point P (2,2), circle C: x2 + y2-8y = 0, the moving straight line L passing through point P intersects with circle C at two points a and B, the midpoint of line AB is m, and O is the coordinate origin to find the trajectory equation of M
- 12. Given p (1,2) and circle C: x2 + y2 = 9, make two mutually perpendicular chords through p to intersect C at a and B, and find the trajectory equation of the midpoint of line ab
- 13. Given that m (x, y) is any point on the circle x ^ 2 + y ^ 2 = 1, find the value range of Y / (x + 2) This problem appears in the section of standard equation of circle. Thank you here
- 14. If the point P (a, b) is a common point of the straight line x + y = 1 / M and the circle x2 + y2 = 2 / M + 1 / m2, then the value range of AB is
- 15. Given that circle C1: x2 + y2-2mx + M2 = 4, circle C2: x2 + Y2 + 2x-2my = 8-m2 (M > 3), the positional relationship between the two circles is () A. Intersection B. inscribed C. circumscribed D. separation
- 16. If the equation x square + y square + 2mx-2y + m square + 5m = 0 represents a circle, find the value range of real number m? Who knows?
- 17. If the equation of a circle is the square of X, the square of Y, KX 2Y, and the square of k = 0, then the coordinates of the center of a circle are formula x^2+y^2+kx+2y+k^2＝0 (x+k/2)^2+(y+1)^2=1-(3/4)k^2 The circle has the largest area That is, the maximum radius That is, 1 - (3 / 4) k ^ 2 is the largest Then k = 0 Center (0, - 1) radius 1 X ^ 2 + (y + 1) ^ 2 = 1 1 - (3 / 4) k ^ 2 max Then how can we get k = 0
- 18. Given that the line L: x-2y-5 = 0 and the circle C: x + y = 50, find (1) the coordinates of intersection a and B, and (2) the area of △ AOB Such as the title, to complete the thinking and process
- 19. Given the circle x2 + Y2 + KX + 2Y = - K2, when the area of the circle is the largest, the coordinate of the center of the circle is______ ．
- 20. The straight line passing through the point P (- 2,3) is cut by the circle X & sup2; + Y & sup2; - 4x + 2y-2 = 0, and the linear equation of the longest chord is obtained