the straight line 2x_3y-4=0 and the circle2x^2+2y^2-4x+7y-16=0 intersect at m and n.find y coordinate of the mid point of mn.do it with full step by step calculation
Question
the straight line 2x_3y-4=0 and the circle2x^2+2y^2-4x+7y-16=0 intersect at m and n.find y coordinate of the mid point of mn.do it with full step by step calculation
Solution
First, let's simplify the given equations.
The equation of the line 2x - 3y - 4 = 0 can be rewritten as y = (2/3)x - 4/3.
The equation of the circle 2x^2 + 2y^2 - 4x + 7y - 16 = 0 can be rewritten as x^2 + y^2 - 2x + 7/2*y - 8 = 0.
Now, substitute y from the line equation into the circle equation:
x^2 + ((2/3)x - 4/3)^2 - 2x + 7/2*(2/3)x - 8 = 0.
Simplify this equation to find the x-coordinates of points M and N.
Once you have the x-coordinates, substitute them back into the line equation to find the corresponding y-coordinates.
Finally, the y-coordinate of the midpoint of MN is the average of the y-coordinates of M and N, which can be found by adding the two y-coordinates and dividing by 2.
Similar Questions
Find the midpoint M of the line segment joining the points A = −8, 2 and B = −4, 4.
find the coordinates of the points of intersaction of the straight line of the staight line5x-4y+25=0 and the circle 2x^2+2y^2+7x-6Y-15=0.do it with full calculations
The coordinates of the midpoint of segment M N are 4 comma 1. The coordinates of point M are negative 2 comma 5. What are the coordinates of point N?
a straight line l intersects the circle 4x^2 +4y^2+18x-12y-2=0 at 2 points p and q.the slope of l is 3/4.if l passes through3,7,find the coordinates of p and q and the equation of the diameter which is perpendicular to l.do with full calculations
If the line 3 x − 4 y = m cuts the circle x 2 + y 2 − 4 x − 8 y − 5 = 0 in two points then limits of m are
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.