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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
The best answer is 1, x = 2Y + 5 into 5Y + 20Y + 25 = 50, y + 4y-5 = 0, y = 1, y = - 5, x = 2Y + 5, so a (7,1), B (- 5, - 5) 2, ab = √ [(7 + 5) + (1 + 5)] = 6 √ 5, the distance from O to L = | 0-0-5 | / √ (1 + 2) = √ 5, the bottom edge is 6 √ 5, the height is 5, so the area is 15
The equation of the circle with the intersection of the straight line x + 3y-7 = 0 and the known circle X & sup2; + Y & sup2; + 2x-2y-3 = 0 and the sum of the four intercepts on the two coordinate axes is - 8 is obtained
X + 3y-7 = 0 and the known circle X & sup2; + Y & sup2; + 2x-2y-3 = 0 intersection (1,2) (- 2,3) assumption: the equation of the circle (x-a) ^ 2 + (y-b) ^ 2 = R ^ 2x = 0, y ^ 2-2by + A ^ 2 + B ^ 2-r ^ 2 = 0, Y axis intercept Y1 + y2 = 2by = 0, x ^ 2-2ax + A ^ 2 + B ^ 2-r ^ 2 = 0, X axis intercept X1 + x2 = 2A, so: 2A + 2B = - 8, (1-A) ^ 2 + (2-B)
{(x+2y)(x-2y)+[2(x-y)]²｝÷6x=?
The original formula = (X & # 178; - 4Y & # 178; + 4x & # 178; - 8xy + 4Y & # 178;) / 6x
=(5x²-8xy)÷6x
=(5x-8y)/6
RELATED INFORMATIONS
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- 2. 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?
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- 4. 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
- 5. 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
- 6. 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
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- 8. 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,
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- 10. 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
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- 12. 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
- 13. Find the linear equation of the longest and shortest chord of a point P (3,1) in the circle X & sup2; + Y & sup2; - 8x-2y + 8 = 0
- 14. Given that the point m is on the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1, the circle centered on M is tangent to the X axis and the right focus F of the ellipse, if the circle m is compared with the Y axis A. B two points, and the triangle ABM is an equilateral triangle with side length 2, the equation for solving ellipse
- 15. Given that the line L: x + Y-9 = 0 and the circle M: 2x & sup2; + 2Y & sup2; - 8x-8y-1 = 0, the point a (4, Y0) is on the line L, B and C are two points on the circle M In the triangle ABC, ∠ BCA = 45 ° AB passes through the center of circle m, then the distance from the center of circle m to the straight line AC is
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