Given that point P is a point outside the circle C: x ^ 2 + y ^ 2 = 1, let K1 and K2 be the slopes of two tangent lines of circle C passing through point P K1 * K2 = - λ (λ does not = - 1,0), find the equation of the locus m of point P, and point out the type of conic where the curve m lies | Math enthusiast | Mathematical art

Given that point P is a point outside the circle C: x ^ 2 + y ^ 2 = 1, let K1 and K2 be the slopes of two tangent lines of circle C passing through point P K1 * K2 = - λ (λ does not = - 1,0), find the equation of the locus m of point P, and point out the type of conic where the curve m lies

Let P (a, b)
Then the line y = K (x-a) + B
(│k*0-0+b-ak│)/(k^2+1)=1
The equation: K ^ 2 (a ^ 2-1) - 2abk + B ^ 2-1 = 0
And K1 * K2 = - μ
That is, (b ^ 2-1) / (a ^ 2-1) = - μ
B ^ 2 + μ a ^ 2 = μ + 1 (μ > 1)
That is, P trajectory m is: μ x ^ 2 + y ^ 2 = μ + 1 (μ > 1)
ellipse

RELATED INFORMATIONS

1. Is 2000 a leap year? Because leap year is divisible by 4, but not by 100, or divisible by 4, and divisible by 400 Push like this, 2000 is and is not? Who can explain why? How do you explain my definition?
2. What month is the average maximum temperature in the southern hemisphere
3. There is a problem: evaluate 1 / 3 (- 3x ^ 2 = 6x-12) - 1 / 2 (4x-2x ^ 2), where x = 2010, But his calculation is also correct. What do you think is the matter?
4. 2005*3/8—0.375*1949+3.75*10.4
5. Seven fifths of an hour equals () hours How to calculate Seven fifths of an hour equals () hours One sixth of five thousand meters equals () kilometers Two thirds of 15 yuan is () yuan One half of two thousand meters is () meters fraction
6. 76 * (1 / 23-1 / 53) + 23 * (1 / 53 + 1 / 76) + 53 * (1 / 23-1 / 76), please explain the reason, thank you!
7. 0.375=9( )=______ ÷16=______ ：8=______ %
8. One in seven times three times two in seventeen If you can calculate simply, you can calculate simply
9. What is 364.3 and 15.4?
10. What is the least common multiple of 63, 27 and 36
11. 1. Draw a secant from a point outside the circle P (1,1) to the circle x2 + y2 = 1, intersect the circle at two points a and B, and find the trajectory equation of the midpoint of the chord ab
12. In the plane rectangular coordinate system, the coordinates of the end point of the line AB are a (- 2,4), B (4,2), and the line y = kx-2 always has an intersection with the line. The value range of K is calculated After taking the endpoint coordinates in, we can calculate k = 1 and K = - 3. Why should it be greater than or equal to 1 and less than or equal to - 3
13. When t belongs to R, the graph represented by parameter equation x = (- 8t) / (4 + T ^ 2), y = (4-T ^ 2) / (4 + T ^ 2) is____
14. If the circle x2 + y2 = 4, a (- 1,0) and B (1,0) move the parabola through two points a and B, and the tangent of the circle is taken as the guide line, then the focus trajectory equation of the parabola is () A. x25+y23＝1(y≠0)B. x24+y23＝1(y≠0)C. x25+y24＝1(y≠0)D. x23+y24＝1(y≠0)
15. If there is a common point between the line L passing through point a (4,0) and the curve (X-2) 2 + y2 = 1, the range of the slope of the line L is () A. [−3，3]B. (−3，3)C. [−33，33]D. (−33，33)
16. As shown in the figure, it is known that in isosceles △ ABC, ab = AC, P and Q are points on edge AC and ab respectively, and AP = PQ = QB = BC=______ ．
17. Let a + B + C = 1 vector OP = a vector OA + B vector ob + C vector OC, how can we prove that p a B C four points are coplanar?
18. The area of the figure enclosed by the curve expressed by the equation | x | + | y | = 1 is () A. 2B. 2C. 1D. 4
19. The area of the figure enclosed by the curve y = x & # 178; - 1 and X axis is equal to
20. Find the area a of the figure enclosed by the curve y = e ^ x, y = 2 and x = 0, and the volume of one revolution around the Y axis Using the knowledge of definite integral,