14th one

Dear Student,
Please find below the solution to the asked query:

We have9x2+25y2=2259x2225+25y2225=1x225+y29=1...iStandard equation of ellipse is x2a2+y2b2=1a2=25a=5b2=9b=3Ends of latus ractum are ae,b2a,ae,-b2a,-ae,b2a,-ae,-b2ae=a2-b2a2=25-925=45ae,b2a=5×45,95=4,95ae,-b2a=5×45,-95=4,-95-ae,b2a=-5×45,95=-4,95-ae,-b2a=-5×45,-95=-4,-95Equation of tangent to i at x1,y1 isxx125+yy116=1Now just put above four points in place of x1,y1 to getfour equations of tangents.

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