Prove that for all values of `theta`
, the locus of the point of intersection of the lines `xcostheta+ysintheta=a`
and `xsintheta-ycostheta=b`
is a circle.
Text Solution
Verified by Experts
Since the point of intersection satisfies both the given lines, we can find the locus by eliminating `theta` from the given equation. Therefore, by squaring and adding, we get equation `x^(2)+y^(2)=a^(2)+b^(2)` which is the equation of circle.
Show that the locus of the pt of intersection of the st.lines xcostheta+ysintheta=a and xsintheta-ycostheta=b is a circle.
Whatever be the values of theta , prove that the locus of a point of intersection of the lines x cos theta + y sin theta = a and x sin theta - y cos theta = b is a circle.
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If theta is a variable and a,b are constants then find the locus of the point of intersection of the lines xsintheta+ycostheta=aandxcostheta-ysintheta=b .
Whatever be the values of theta , prove that the locus of the point of intersection of the straight lines y = x tan theta and x sin^(3) theta + y cos theta = a sin^(3) theta cos theta is a circle. Find the equation of the circle.
For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is
The equation of the locus of the point of intersection of the straight lines x sin theta + (1- cos theta) y = a sin theta and x sin theta -(1+ cos theta) y + a sin theta =0 is:
Show that the locus of the point of intersection of the lines x cos alpha + y sin alpha = a and x sin alpha - y cos alpha = a , when alpha varies, is a circle.
