AT HOME CORP
424B3, 1999-12-07
COMPUTER PROGRAMMING, DATA PROCESSING, ETC.
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<PAGE>   1

PROSPECTUS SUPPLEMENT #10                       FILED PURSUANT TO RULE 424(B)(3)
(TO PROSPECTUS DATED JULY 2, 1999 AND                 REGISTRATION NO. 333-78419
SUPPLEMENT DATED JULY 15, 1999)

                                EXCITE@HOME LOGO

                              AT HOME CORPORATION

                   $437,000,000 PRINCIPAL AMOUNT AT MATURITY
                  CONVERTIBLE SUBORDINATED DEBENTURES DUE 2018

                        SHARES OF SERIES A COMMON STOCK
                   ISSUABLE UPON CONVERSION OF THE DEBENTURES
                           -------------------------

     This prospectus supplement relates to the resale by the holders of
convertible subordinated debentures due 2018 of Excite@Home and the shares of
Series A common stock of Excite@Home issuable upon the conversion of the
debentures.

     You should read this prospectus supplement in conjunction with the
prospectus dated July 2, 1999 and prospectus supplement dated July 15, 1999,
each of which is to be delivered with this prospectus supplement. All
capitalized terms used but not defined in this prospectus supplement shall have
the meanings given to them in the prospectus.

     The information in the table appearing under the heading "Selling
Securityholders" in the prospectus is superseded in part by the information
appearing in the table below.

<TABLE>
<CAPTION>
                                                 PRINCIPAL AMOUNT OF
                                                     DEBENTURES         PERCENTAGE OF    SHARES OF SERIES A
                                                 BENEFICIALLY OWNED      DEBENTURES      COMMON STOCK THAT
                     NAME                         THAT MAY BE SOLD       OUTSTANDING        MAY BE SOLD
                     ----                        -------------------    -------------    ------------------
<S>                                              <C>                    <C>              <C>
Merrill Lynch Pierce Fenner & Smith Inc........      $9,344,000              2.1%             122,406
Goldman Sachs & Co.............................      $4,940,000              1.1%              64,714
J. P. Morgan Securities Inc....................      $3,275,000                *               42,902
Forest Global Convertible Fund Series A5.......      $3,430,000                *               44,933
Forest Fulcrum Fund............................      $3,080,000                *               40,348
Forest Alternative Strategies Fund Series
  A5I..........................................      $  210,000                *                2,751
Forest Alternative Strategies Fund Series
  A5M..........................................      $   70,000                *                  917
</TABLE>

- -------------------------
* Less than 1%.
                           -------------------------

     INVESTING IN OUR CONVERTIBLE SUBORDINATED DEBENTURES OR OUR SERIES A COMMON
STOCK INVOLVES A HIGH DEGREE OF RISK. PLEASE CAREFULLY CONSIDER THE "RISK
FACTORS" BEGINNING ON PAGE 6 OF THE PROSPECTUS.

     NEITHER THE SECURITIES AND EXCHANGE COMMISSION NOR ANY STATE SECURITIES
COMMISSION HAS APPROVED OR DISAPPROVED OF THESE SECURITIES OR PASSED UPON THE
ADEQUACY OR ACCURACY OF THIS PROSPECTUS OR THIS PROSPECTUS SUPPLEMENT. ANY
REPRESENTATION TO THE CONTRARY IS A CRIMINAL OFFENSE.

          The date of this prospectus supplement is December 7, 1999.


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