Find the tangent plane and normal equation of surface 3x ^ 2 + y ^ 2-z ^ 2 = 3 at point P (1,1,1)

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• 1. The equation for finding the projection line of the line 2x-4y + Z = 0,3x-y-2z-1 = 0 on the plane X-Y + Z = 2
• 2. When a plane passes through two points (2,2,1) and (- 1,1, - 1), it is perpendicular to another plane 2x-3y + Z = 3. Find the equation of the first plane
• 3. In the rectangular coordinate plane, the distance from a moving point P on the right side of the y-axis to the point (1 / 2,0) is 1 / 2 larger than the distance from it to the y-axis The equation for finding the locus C of the moving point P Let Q be a moving point on the curve C, and the points B and C are on the y-axis. If the triangle QBC is a circumscribed triangle of circle (x-1) ^ 2 + y ^ 2, the minimum area of the triangle QBC is obtained
• 4. In the rectangular coordinate plane, the distance from a moving point P on the right side of the y-axis to the point (1 / 2,0) is 1 / 2 larger than the distance from it to the y-axis The equation for finding the locus C of the moving point P
• 5. In the second diagnosis! In the rectangular coordinate plane, the distance from a moving point P on the right side of the y-axis to the point (1 / 2,0) is 1 / 2 larger than the distance from it to the y-axis, so the trajectory C of the moving point P is called
• 6. It is known that the difference between the distance from a moving point P to point F (1.0) in the plane and the distance from point P to y axis is equal to 1 The equation for finding the locus C of the moving point P
• 7. It is known that the difference between the distance from a moving point P to point F (1,0) and the distance from point P to Y-axis is 1 The equation for finding the locus C of the moving point P Through point F, make two lines L1 and L2 whose slopes exist and are perpendicular to each other. Let L1 intersect with trajectory C at points a, B and L2 and intersect with trajectory C at points c and D. find the minimum value of vector ad multiplied by vector EB
• 8. In the same plane, the distance from the known point O to the straight line L is 5. Draw a circle with the center of the circle and the radius of R. when r =? There are only three points on the circle O whose distance to the straight line L is equal to 3?
• 9. If the three planes are perpendicular to each other, their three intersecting lines intersect at point O, and the distances from a point P in space to the three intersecting lines are 2,5 ^ (1 / 2) and 7 ^ (1 / 2), respectively, then the length of OP is
• 10. If we know that plane α ‖ plane β, line L ⊂ plane α, point P ∈ line L, and the distance between planes α and β is 8, then the distance to point P in β is 10, and the trajectory of the point with the distance to l of 9 is () A. A circle B. four points C. two straight lines D. two points
• 11. Find the section equation of the square of surface y * 2 = x * 2 + Z at point (3,5,4)
• 12. Find the section equation of surface e with Z power - Z + xy = 3 at point (2,1,0)
• 13. Section equation of a curved surface cut by a plane Such as the title. If x ^ 2 + y ^ 2 + Z ^ 2 = 4 is cut by X + y + Z = 0, what is the section equation? I don't want to draw. I want to see pure algebra, because there are many complex drawings that can't be drawn
• 14. In this paper, the binary quadratic equation x ^ 2-3xy + 2Y ^ 2 = 0 is transformed into two linear equations
• 15. Tangent plane equation of surface x ^ 2 + 2Y ^ 2 + Z ^ 2 = 12 at point (1,1, - 3)
• 16. What is the integer solution of the equation 2x ^ 2-3xy-2y ^ 2-98 = 0
• 17. Find the tangent plane and normal equation of the surface X & # 178; + 2Y & # 178; + 3Z & # 178; = 21 at the point (- 1, - 2,2)
• 18. Find a point on the ellipse x ^ 2 + 4Y ^ 2 = 4 to make it the shortest distance to the plane 2x + 3y-6 = 0
• 19. The distance between X + 2y-4 = 0 and 2x + 4Y + 5 = 0 is
• 20. Find a point on the ellipse x ^ 2 + 4Y ^ 2 = 4 to make it the shortest distance to the plane 2x + 3y-6 = 0