A comet has a parabolic orbit with the sun at its focus When

A comet has a parabolic orbit with the sun at its focus. When the comet is 100 squareroot 2 million miles from the sun, the line for the sun to the comet makes an angle of 45 with the axis of the parabola as shown in the following figure. What will be the minimum distance from the comet to the sun. The orbit of the earth is an ellipse with the sun at one focus. The planet\'s maximum distance from the sun is 94.56 million miles and its minimum distance is 91.45 million miles. What are the lengths of the major and minor semiaxes of the earth\'s orbit, and what is the eccentricity? Identify and sketch the graph of x^2 = 2(x + y + 2).

Solution

Solution: let suppose focus is origin

the point of comet is 100cos45 & 100sin45

the parabola eq. is y²=4a(x+a)

the minimum distence is a which is to be distence between focus and center, parabola satisfai to the point and we get a=20.7 million meter

5):the given maximum distence is 94.56 and minimum distenc is 91.45

let a is semi-major distence & b is semi-minor distence

maximum distence is a+(a²+b²)^1/2=94.56 & minimum distence a-(a²+b²)^1/2=91.45

after solving we get a=93.0004 million meter & b=92.87 million meter

eccentricity e=c/a                                                                                c=+(a²+b²)^1/2

e=0.016

6):

and this is parabola centare at (1,-5/2)  

parabola is (x-1)²=2y+5 and this parabola is symmetric about x=1, parabola inc. upper side of y-axis