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If the projection of origin o on line L is point H (- 2,1), then the equation of line L is Please don't use the slope method. We haven't learned that yet. Use the normal vector or direction vector method
Since the vector Oh = (- 2,1), the direction vector (perpendicular to OH) can be (1,2). According to the parametric equation, the equation of the straight line l can be obtained as follows:
X = - 2 + T, y = 1 + 2T, the elimination parameter is 2x-y + 5 = 0
When the line L passes through the point m (2,1) and intersects the positive half axis of x-axis and y-axis at two points a and B respectively, O is the coordinate origin. (I) when the area of △ OAB is the smallest, the equation of line L is obtained. (II) when | Ma | · | MB | is the minimum, the equation of line L is obtained
(1) Let the linear equation l be XA + Yb = 1 (a, B are positive numbers), ∵ l pass through the point m (2, 1), ∵ 2A + 1b = 1. ∵ 1 = 2A + 1b ≥ 22a · 1b, then ab ≥ 8 is obtained. If and only if 2A = 1b, i.e. a = 4, B = 2, the equal sign holds. If a = 4, B = 2, AB has the minimum value of 8, and △ OAB area is s = 12ab =
-Are 3xy and y of the same kind
No
RELATED INFORMATIONS
- 1. In the equation 3x ay = 8, if x = 3Y = 1 is one of its solutions, then the value of a is______ ．
- 2. It is known that P (x, y) is a moving point on the circle C: x + y-2y = 0. If x + y + m ≥ 0 is constant, the value range of real number m is obtained
- 3. Given the curve C: x2 + y2-2x-4y + M = 0. (1) when the value of M is, the curve C represents a circle; (2) if the curve C and the straight line x + 2y-4 = 0 intersect at two points m and N, and OM ⊥ on (o is the origin of the coordinate), find the value of M
- 4. Given that the circle m is tangent to the x-axis, the center of the circle is on the straight line x-2y = 0, and the maximum distance from the moving point on the circle m to the y-axis is 3, find the square of the circle M
- 5. Circle x ^ + y ^ = 1 and circle x ^ + y ^ - 2x-2y = 0, the position relation is? (^ is 2, that is, x square or Y Square) So R + r = 1 + radical 2, but I calculate that the distance between the two center points is = radical 2. Why is it tangent??? The distance between the center of the circle is less than the sum of the radii, so it intersects!!!!!
- 6. It is known that the straight line X-Y + 3 = 0 and the circle x + y = 1. Judge their position relation and prove it
- 7. Given that P is any point of the circle C: x ^ 2 + y ^ 2 + 4x + ay-5 = 0, the symmetric point of P about 2x + Y-1 = 0d is still on the circle
- 8. Ask for help high school "basic inequality" problem: known circle C: the square of X + the square of Y + BX + ay-3 = 0 (a, B are positive real numbers) on any point about the straight line L: 1 Given that any point on the circle C: x square + y square + BX + ay-3 = 0 (a, B are positive real numbers) with respect to the symmetric point of the line L: x + y + 2 = 0 is on the circle C, then the minimum value of 1 / A + 3 / B is___ .
- 9. Let the center of the circle x ^ 2 + y ^ 2-4x + 2y-11 = 0 be a and the point p be on the circle, then the trajectory equation of the midpoint m of PA is
- 10. (2010` Guangzhou the first mock exam) the known moving circle C passes through point A (-2,0) and is cut in with the circle M: (X-2) ^2+y^2=64. (1) Find the trajectory equation of the center of moving circle C (2) Let L: y = KX + m (where k, m ∈ z) and (1) intersect at two different points B and D, and hyperbola (x ^ 2) / 4 - (y ^ 2) / 12 = 1 intersect at two different points e F. ask if there is a straight line L such that vector DF (vector) + be (vector) = 0 (vector). If there are, please point out how many such lines. If not, please explain the reason
- 11. When ma * MB is the minimum value, the equation of line L is obtained
- 12. If the area of △ AOB (o is the coordinate origin) is 2, then the value of B is?
- 13. Given that the point P (m, n) is on the straight line x = - 1, and the point P is symmetrical about the origin of the coordinate is on the straight line y = 3, the coordinate of P is obtained
- 14. When m is equal to what, the inequality mx5
- 15. Known inequality (MX)_ 1) The solution set of (x + 2) > 0 is - 3
- 16. Given that the line x + 2y-3 = 0, the intersection circle x ^ 2 + y ^ 2 + x-6y + F = 0 is at the point P, Q, O, and OP is perpendicular to OQ, then f is?
- 17. If the distance between the point P (m, 3) and the line 4x-3y + 1 = 0 is 4, and the point P is in the inequality 2x + y
- 18. If there is only one point between the origin and point (1,1) in the plane region represented by inequality 2x-y + a > 0, then the value range of a is larger
- 19. If s = 2x = Y-Z, the range of S is obtained
- 20. If 1 / X-1 / y = 2, find the value of (3x-2xy-3y) / (x-2y-y)