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Let (x, y) be the point of ellipse x ^ 2 / 16 + y ^ 2 / 9 = 1, then what is the maximum value of 3x-4y ___________ thank you
Let x = 4cost, y = 3sint
3x-4y = 12 (cost Sint) = 12 * radical 2 (cost + 45 degrees)
The maximum and minimum values of the absolute value of PQ are (), respectively, if P is on the circle x ^ 2 + y ^ 2 = 4 and Q is on the circle x ^ 2 + y ^ 2 + 4x-4y = 0
x^2+y^2+4x-4y=0
==>
(x+2)^2+(y-2)^2=8
The centers of the two circles are o (0,0), C (- 2,2)
The radius is R1 = 2, R2 = 2 √ 2
|OC|=2√2
If the chord PQ passing through the left focus of the ellipse is perpendicular to the major axis, if f is the right focus and PF is perpendicular to QF, what is the eccentricity of the ellipse
The square root of 2 minus 1
Let the elliptic equation be (x / a) 2 + (Y / b) 2 = 1, B2 + C2 = A2
Substituting x = C, we get
y2=（a2-c2）*b2/a2
It is easy to know that PQF is an isosceles right triangle
That is, y2 = C2
Simplify, simplify
（a2-c2）2=4a2c2
a4-6a2c2+c4=0
Divide both sides by A4, and you get
e4-6e2+1=0
E2 = 3 - (square root of 2)
The square root of E = 2-1
Find the chord length of a straight line passing through the origin with an inclination angle of 45 ° cut by the circle X & sup2; + Y & sup2; - 4Y = 0
It's troublesome to find the way to solve the problem. I just don't understand the problem
Find the chord length of a straight line passing through the origin with an inclination angle of 45 ° cut by the circle x2 + y2-4y = 0
Analysis: ∵ circle x2 + y2-4y = 0 = = > x2 + (Y-2) 2 = 4, Center (0,2), radius 2
A straight line passing through the origin with an inclination angle of 45 ° y = x
The simultaneous solution of them is X1 = 0, Y1 = 0; x2 = 2, y2 = 2
Then the chord length is √ [(y2-y1) + (x2-x1) ^ 2] = 2 √ 2
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